Simplifying Rational Expressions… How? (NancyPi)

Published on July 2, 2018 by

Description: MIT grad shows how to simplify a rational expression. To skip ahead: 1) for how to simplify an expression with DIFFERENCE of SQUARES factoring in it (x^2 - 49), skip to time 1:01. 2) for how to write the CONDITION or RESTRICTION, skip to time 3:52. 3) for how to simplify an expression with QUADRATIC(s) in it (like the x^2 - 3x + 2 trinomial), skip to time 6:12. 4) for an example with LARGER COEFFICIENTS and a NEGATIVE x^2 term (like -20x^2 + 14x + 12), skip to time 9:57. Nancy formerly of mathbff explains the steps:

For how to FACTOR QUADRATICS, jump to
For how to FIND the DOMAIN of a function, jump to
For more factoring examples in my video on how to solve quadratic equations by FACTORING, jump to:

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There are three steps to simplify algebraic rational expressions:
1) Factor the numerator and denominator as much as possible.
2) Cancel factors that are the same on top and bottom.
3) Write a restriction ("condition") for any x values that used to make the denominator zero, before you cancelled factors. For instance: "x cannot equal -1".

1) FACTOR as much as you can: Factor the top and bottom as much as possible. In both the numerator and denominator, always check first if there's a number or a variable (x) that is in all the terms that you can pull out front. If you have something that looks like "x^2 minus a perfect square number", like x^2 - 9, you can factor using the difference of squares formula, into (x + 3)(x - 3). If you have a difference of cubes (x^3 - 8) or sum of cubes (x^3 + 27), you can factor using the sum/difference of cubes formulas. If you have a quadratic expression on top or bottom that has three terms ("trinomial"), you can factor it using trial and error, or the "magic x" trick for factoring. To learn how to factor quadratics, check out my video on factoring.

2) CANCEL: Cross out any factors that are the same on top and bottom, and write what's left behind. When you've cancelled everything you can, you now have your simplified rational expression, or expression "reduced to lowest terms" or in "simplest form".

3) CONDITION: Is that all? To be technically correct, you should also write a note next to the simplified rational expression that states the restriction. You can check with your teacher to see if you’re required to write it for your class. But either way, the restriction is there, and the final answer isn’t really complete without this “condition”. All you need to do is: look at any factor(s) you cancelled in the denominator (ex: x-7), see what x value used to make that factor equal to zero (7), and next to your answer write “x not equal to” that number (x not equal to 7).

We put the restriction, or condition, there at the end, because if we didn’t, the restricted x value would appear to be a valid x value for the expression, when it’s not. When we simplified the expression by cancelling the bottom factor, we got rid of the undefined, division-by-zero problem for that x-value, but in reality that x-value is still not allowed. So to be totally correct, write the note that states this restriction next to your answer.

For how to find the HORIZONTAL ASYMPTOTE of a rational function, jump to

For more math help and videos, check out:

Edited by Miriam Nielsen of zentouro:

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  • mereal abin creations 5 years ago

    first to comment….. Great video…..This is very helping…..

  • Adhiraj V. 5 years ago

    Lol I’m a 12th grade student still I watched the full video. Good stuff!

    • Axando Aldria 3 years ago

      Which grade is this for?

    • Ram Sharma 3 years ago

      yeah which grade is this for son give the lady an answer

  • Bruno Viana 5 years ago

    I love it! ❤ A hug from Brazil, Nancy.

  • Rongfang Li 5 years ago

    You are back!!

  • Sebastian 5 years ago


  • Motorola Nova 5 years ago

    You’re a natural educator.

    • Don Melaraya 5 years ago

      Motorola Nova … and rational.

  • Happy Life WISH 5 years ago


  • Hussaan Alvi 5 years ago

    It’s easy, it really helps in Intergration specially in partial fraction !

  • Jerry Cheng 5 years ago

    Thanks for coming back Nancy! I found your calc lectures really helpful

    • Rebecca Amodeo 5 years ago

      Jerry’s Studio agreed!

  • Haram 5 years ago

    just here to support <3

  • Wil N 5 years ago

    I’m glad you are still making videos, the new girl on MathBFF is alright but she is no NancyPi.

    • crafty girl 5 years ago

      William Nield ur right

    • Mirriam Hakobwa 4 years ago

      I love you Nancy

  • Mohsin Jawaid 5 years ago

    Very use full Nancy …👍👍❤

  • Fredde 5 years ago

    Can u do a video about 3d curl?

  • EVFU 10 5 years ago

    Thank you.

  • Faisal 5 years ago

    I really love ur videos, great job keep it up REEEEEEEEEEEEEEEEEEEEEEEE

  • Abdulaziz Abdullah 5 years ago

    Awesome ✔✔👍👍👌👌

  • Johnny Huff 5 years ago

    Question Nancy…wouldn’t you always want to remove the “x” from the denominator…or is that just in Calculus?

  • SpiralMX 5 years ago

    you are back ! .. and i love it <3

  • Andres Falcon 5 years ago

    Hi Nancy, I am looking for more advance calculus videos, do you know any channel about it? Thanks a lot… great vidios, way to go.

  • Leonardo Camargo 5 years ago

    I rather watch this than the world cup.

    • Díaz 5 years ago

      Same. 😀

    • MP 5 years ago


    • Gabriel Flores 4 years ago

      wo wo wo wo really???? well yea u right.

  • maller91 5 years ago

    Great! More videos like this!

  • rdknight89 5 years ago

    You’ll always be my math bff <3

  • Abdal Syed 5 years ago

    So fine

  • Shaun Donovan 5 years ago

    Hi Nancy, thanks for the great video. I am having trouble with factoring the final example when you get (5x-6)(3x+2). Do you know wher I am going wrong or where to look for assistance

  • Ganesh Jainarain 5 years ago

    Do some Calc! I’m struggling with related rates 🙁 💓

  • sgedeon01 5 years ago

    I love Nancy Pi. Thanks for all the great videos

  • Sal7_one 5 years ago

    Thank you, honestly i can’t believe how much you’ve helped me i passed so easily with your help

  • Hudson Stronck 5 years ago

    done with math for now… still watching lol

    • Lockz 2k 3 years ago

      @Cassi Nova lmaoo

    • Rizzo 3 years ago


    • Franck's Notes 3 years ago

      I got more video in my channel if you’re looking for more to binge watch 👀

    • Rizzo 3 years ago

      @Franck’s Notes stfu

    • Ok 3 years ago

      @Rizzo bruh

  • D really 5 years ago

    Yeah , I wanted to be done at 4:00, and Yeah, I know you want a good nights sleep, so Yeah,,, We both have to do the right thing.

  • Rebecca Amodeo 5 years ago

    Thanks for helping prevent summer slide on my math skills!

    • Maths class KI 4 years ago


  • José Vivas 5 years ago

    Hellooooooooooooooooooo Nancy! I missed you 🙁 XD. I love your videos. You are the best 😉 :*

  • Dave CGS 5 years ago

    Can you put back the Magic X video on factoring. It was fantastic.

  • global terroil 5 years ago


  • Dr Scott 5 years ago

    Your videos have really become much more funny over the year. I like your humor

  • roberson644 5 years ago

    I already have all my math units completed, why am I still watching this?

  • OrphanPaper 5 years ago

    you conciser them Rational obversely I need hours and hours of readjustments

  • Miguel Angel Ponce 5 years ago

    great job, greetings from Mexico

  • MinecraftPanda8 5 years ago

    Im so glad you make videos! I would honestly not have passed pre-calc if it wasnt for your vids.

  • !!!!???? 5 years ago

    another great vid Nancy thank you. i have been watching you videos for years now and i have to say this is the happiest i have ever seen you in one. thanks for helping me pass calculas this past term. please keep’em coming. thank you

  • Daniel Dorantes 5 years ago

    Thank you Nancy! Would have never succeeded in calculus without your videos, keep up the great work!

  • 551223 5 years ago

    Do calc 2 videos!!

  • Jabrils 5 years ago


    • NancyPi 5 years ago

      JABRILS! 🙋🏻

  • James Parlane 5 years ago

    But Whyyyyyyyyyyyyyy?????????

  • James Parlane 5 years ago

    I try to understand but just can’t. its like when Seinfeld went out with newmans x

  • ListentoGallegos 5 years ago

    removable singularities? is it permissible to let x=1 or x=7 because its usually in a limit where x is approaching but not equal to the number that makes the function undefined?

  • Maths With Melv 5 years ago

    Big fan of your work!

  • ImKurono 5 years ago

    My math bae 😀

  • Onihikage 5 years ago

    It’s good to hear your voice again, Nancy! I love what you’ve done in the description, it’s like a typical math course session, and definitely more search engine friendly for struggling students. Someday your channel could be all a body needs to learn advanced math!

  • Jozef Aerts Wiskunde 5 years ago

    I do not understand how you factorize the terms ? Just guessing ? Why 5x-6 ? Just quessing ? Why not 5x-3 ?

  • Playgrl966 5 years ago

    You need to be a math teacher. You have a natural gift. You not only show how you do the math, but you explain it very well so that you understand how to rationalize the steps though the problem.
    You got me
    Through trig and calculus! Thank you!!

  • Tamojit Das 5 years ago

    Thank you ma’am!!!

  • battlefield6789 5 years ago

    Yesss I love you and your video 😘

  • MrRockGemios 5 years ago

    I love her so much

  • KürşatHoca 5 years ago

    Hı nancy , ı am a math teacher , could you explain me , which system do you use to make videos,

  • Frank Mwiti 5 years ago

    Hi Nancy, could you please kindly let me know how/what you use to project the lessons when you write? Is it like a mirror whiteboard or how do you do it?

  • Abel Lopez 5 years ago

    😍😁 awesome.

  • Chaminda Silva 5 years ago

    Thanks for teaching me how to simplify a rational expression.
    Angel Nancy,
    Why is 1/0 undefined? Please explain me.
    2nd example contains a hole at X=1 and also there is another restriction at X=-6.
    Nancy,Isn’t it?

  • Ciras Alcilian 5 years ago


  • Ubi Bhatt 5 years ago

    Hi @NancyPi, can you make video on definition of polynomial? i.e. what makes a algebraic express a polynomial.

  • Brandon Gonzalez 5 years ago

    I had no idea your original conditions still remain after simplification, I thought the purpose was to adjust the expression so that there would no longer be a condition!!! Thank you Nancy, i’m glad you’re back.
    * and I’ve never seen this hilarious quirky side to you! 3:54 — love it.

  • Brandon Gonzalez 5 years ago

    “leave this here like it’s the whole story, fronting like its the same as this ((twitch)) -when its *not* .”

  • James Ferguson 5 years ago

    Can you do a video on delta epsilon proof

  • crafty girl 5 years ago

    Can you please make video of integration with definition and integration as a are of curve. Plz Nancy

  • Grover Smittle 5 years ago

    A couple of questions about the last example: Where does the -10 come from? Doesn’t -6+2=-4? How do you get -8 from that? Please forgive my ignorance—I REALLY struggle with math.

    • Jack Davis 4 years ago

      She factored out -2 from 20, giving negative -10

    • Robert Campbell 3 years ago

      I didn’t watch, but -10 is the difference not the sum.

  • Kevin Thorton 5 years ago

    Hey can you use your maths to create a huge magnetic suit that would allow me to walk on the streets and suck up cars onto the suit.

  • Ollie Pie 5 years ago

    i love nancy i wish i could be her friend

  • Juan Gabriel 5 years ago

    Babe i miss yoy so much

  • arkangelares 5 years ago

    10% of my engineering degree is due to you. Thx

    • BananaNutBread 4 years ago

      @Dejan Zajebancije I was never put into algebra 1 part2 nor algebra 2 or calculus in high-school. But senior year, I passed out of geometry and trig. So after being two/three years into my college career I am only now starting calculus after self-taught algebra starting from basic concept.

    • ne0 3 years ago

      @Dejan Zajebancije Computers do the calculations related to bridges nowadays.

    • Rhazdy Gonzales 3 years ago

      Thank you ma’am you helped me a lot cuz this is the only thing that I can easily understand cuz some of the others is hard so thank you ,you really help a lot

    • Alex Mortiis 3 years ago

      @Dejan Zajebancije xD

    • Franck's Notes 3 years ago

      This is a very nice thing to say

  • HeartforSale 5 years ago

    Nancy you’re such an amazing teacher, I’ve never ever found explanations of maths concepts so engaging and accessible. Thank you so much!

  • LiOnHeLl8121 5 years ago

    Love the work. keep it nancy. You’re the best youtuber when it comes to teaching math.

  • timothy dunbar 5 years ago

    thank you!! you are awsome

  • LiOnHeLl8121 5 years ago

    can you do a series of SAT Math problems.

  • jasmine sebastian 5 years ago


  • Windows Logo 5 years ago

    13:55 lol 😀

  • Saliba T 5 years ago

    Where did you go? Took me years to find this new channel

  • Bassel Alagha 5 years ago

    this chick is so hot i cant focus

  • Caybo Kotze 5 years ago

    You deserves more views.

  • Richard Ray 5 years ago

    I mean absolutely no disrespect whatsoever, but I find myself watching your videos and learning math simply because I find you beautiful, enjoyable, intelligent, and engaging. Keep up the great work. You are an inspiration!!

  • Bts Rapline 5 years ago


  • Hillary Gwenn Del Rosario 5 years ago

    how does she writes it😂

    • Justina Bailey 4 years ago

      she writes normally and then the image gets flipped

  • Abel Lopez 5 years ago

    Fyi I wouldn’t ignore you 🙂.

  • danny cagley 5 years ago

    You helped me tremendously through school. Just graduated this spring with a 3.97 Summa Cum Laude! Thanks for your great help! I recommend you to everyone I know that needs math help. You are awesome!

  • José Ignacio Naranjo 5 years ago

    I love your videos……..all of them are amazing…….thanks a lot……..

  • Ahmed Mzhr 5 years ago

    Please do more integral videos I want to learn please

  • Igotbirdspigeons 4 years ago

    I would make a lustful, slightly misogynist remark for the sake of my immaturity and imminent procrastination to compensate for my only partially existing sex life, but I’ll just like and subscribe instead…

  • Dr. Throwback 4 years ago

    I am just flying through these math problems now!!! Thank you!

  • Phil PBOY 4 years ago

    The maths is great, your personality is sweet… but I just can’t get over *how clean your glass is* .. I mean… its literally cleaner than my laptop screen. In fact..why is your voice so clear.. are you *behind* the glass? Or is there an edge that stops before it reaches you? I came with maths questions… but now… I just have a ton of questions and none of them are maths related, hahah

  • Don Miguel 4 years ago

    Ma’am can you please make a video about derivatives of trigonometric function and derivatives of inverse trigonometric functions

  • AstroNation 4 years ago

    Good work Nancy!

  • Francisco Go 4 years ago

    beautiful and intelligent, perfect

  • Baby Lace 4 years ago

    i think i love math irrationally

  • Dave lowinger 4 years ago

    you know Nancy I changed my name the guys. I know I’m just an old pervert but now I’m much better at math 😉

  • Dr Pedro 4 years ago

    Too hot for a math teacher😍

  • Paul Pritchard 4 years ago

    I am self studying mathematics here and your videos are a goto resource for me as your ability to explain complex concepts simply, and your great conversational teaching style, really gets the idea across.

    Thanks for all the help so far NacyPI

  • Ksnipe 157 4 years ago

    Thank you so much!

  • CrazyAlaskanCoDShot 4 years ago

    I can actually focus on my assignments more when I just listen to her voice in the background XD anybody else agree? So soothing….

  • Jerry Cregan Stark Mathurin 4 years ago

    How does-6 and 2 add to 8?

  • Dr. Peppa 4 years ago

    Doesnt she see what she writes backwards IM CONFUSED

  • D R 4 years ago

    Why is she so hot? I would be daydreaming the entire math period.

    • Ayan Nur 3 years ago

      You pervert is
      Not like she wants u wake up bruv

  • Anthony Banks 4 years ago

    Cute & intelligent, with clarity & a simplified style, you should have taught ALL of my classes, even basketball practice, LOL,!!
    Enjoyed this first video of yours regarding “rational expressions”. I hate algebra & really don’t see the need for it on a everyday basis but
    it’s a graduation requirement, unfortunately. Thanks for your simplified & direct problem solving approach! I will watch your other videos!

  • Carlos Gruber 4 years ago

    Mmm. Talk that talk grl.

  • Carlos Gruber 4 years ago

    Got that brain.

  • Donald Page 4 years ago

    The math instruction would be easier to focus on if you blocked your image from the video. I find you distracting.

  • Dawood Ngalo 4 years ago

    I want to wash your videos even if I don’t know algebra. Pretty

  • Jadon Burge 4 years ago

    Amazing help couldn’t figure it out until this vid 10 outa 10 math help

  • Jake Rodgers 4 years ago


  • meril a 4 years ago

    hi why is it that 4b^2-2a can no longer simplified to 2b^2-a, when you can still divide it by 2???

  • rotartlifnI 4 years ago

    Please stop with the sound effects.

    • Eric Rodriguez 4 years ago

      I like it.

  • Ernesto Caudillo 4 years ago

    Watching Guys do math are so boring to learn off of ,,,but learning from you got my attention just don’t leave out any steps when writing it out 😘

  • Jason.A 4 years ago

    What if you have a negative rational function that is on the numerator, not too sure, plz help

  • Melissa Hernandez 4 years ago

    with the last example, how did you get the 6 and 2 in (5x-6)(3x+2)?? Don’t the two numbers have to equal 12 when multiplied and 8 when subtracted?… 6-2=4?….I’m confused…and it wouldn’t be 4 and 3 bc 4-3=1 and 12-1=11….

    • green eyes 4 years ago


  • Melissa Hernandez 4 years ago

    ok ALSO, on example 3, you “getting lucky” means you put (5x-6)(3x+2) in the correct order? I initially wrote it as
    (5x+2) and (3x-6) and was wrong….

  • Melissa Hernandez 4 years ago

    ALSO on example 3 LOL sorry, why did you choose 5 & 2 and not 10 & 1? what’s the process to figuring that out?

  • XxMesmerized1LOvEXx 4 years ago

    thank you so much you’re a great teacher! <3

    • Usama rafieck 3 years ago

      She makes it easy to understand for me.

  • Our Gucci Life 4 years ago

    Who invited this?!? D;

  • Reubin 4 years ago

    If i had a hot math teacher like this i would never fail a fucking single class

  • Shaddie Jones 4 years ago

    If there was a way to metabolically encapsulate u, I’d gorge u down forever 😊😊

  • rancy boley 4 years ago


  • abc defg 4 years ago

    yo gcse math guys

  • raj k 4 years ago

    Wish u were my teacher !

  • Cliff Williams 4 years ago

    U da best nancy!!!

  • David Wardlow 4 years ago

    Nancy I like all your videos, you are very good.

  • TheZooman22 4 years ago

    I am in my third year of Electrical Engineering at ENMU, and I am watching this. Nancy makes Math fun. I could watch math for hours… I often refer to the video on Logs… we use Logs a lot.

  • JS Ly 4 years ago

    Love your hair. Makes math more interesting, even a little exciting 😉

    • Daniel Lopes 4 years ago

      JS Ly 👀👀

    • Anthony Pagan 3 years ago

      my man ur a perv

  • rama krishna Raju 4 years ago

    Very nice and simple way of explaining. I am tempted to watch your videos because you are more pretty than the problems.

  • josue v 4 years ago

    I love you

  • Michael Austin 4 years ago

    How is she writing backwards 😭

  • Mary Flores 4 years ago

    i think i’ve learned more from you and your videos than all my 21 years of math classes.

  • Stephen Kenny 4 years ago

    I’m in love

  • kamel hatem 4 years ago

    Thank you teacher!!!

  • Dinsmore More 4 years ago

    you are very beautiful I love your voice

  • Dale Putnam 4 years ago

    Please keep making these videos sharing your knowledge. Your awesome

  • Abubacarr Gibba 4 years ago

    I love you, you are great

  • Jerry PEAL 4 years ago

    Ok now my head hurts !

  • jenny mai 4 years ago

    Thank you

  • Pavan Singh 4 years ago

    Forgive me, but on the last one you can also do 15x and x which gives you 15x squared as well, HOW DO YOU KNOW WHICH ONE TO CHOOSE?!

  • Dilwar Hussain 4 years ago

    -6 + 2 = -4 and -6 + 1 = – 5 for Q3) both multiply to get C term but do not add to B term. Tried to FOIL it as well but can’t

  • amoxintubeu 4 years ago

    It is too cute to learn math from you. I have a difficulty to concentrate.

  • josh adams 4 years ago

    Left handed brains beautiful there’s one lucky ass guy out there

    • josh adams 4 years ago

      And I’m about to learn math again lol

  • mila t. 4 years ago

    Please make a video about Partial fraction. I love how clear you can explain things and make math lot easier for me 🙂

  • SFMurchison 4 years ago

    Wow – Thank you! I love your videos

  • Nick Haysgdhakus 4 years ago

    Ur hot

  • Arizona Almazar 4 years ago

    i like how she can relate when math’s confusing LMAO HAHAHA

  • Alessandro Principe 4 years ago

    Who else is watching this before a test?

  • Rasjah Jah 4 years ago

    you are my favorite maths teacher

  • XxMesmerized1LOvEXx 4 years ago

    Ur so adorable!!! Thank u for teaching us ❤️

  • PUBG Gamer 4 years ago

    Thank you 😊

  • apd carson 4 years ago

    greatest time ever learning math!

    • Ayan Nur 3 years ago

      Good for you old man

  • Jeremy Nunez 4 years ago

    Thank you!

  • Jeremy Nunez 4 years ago

    12:30 /6 and -2 don’t add up to -8? was that an error, and they were both supposed to be negative?

    • J Man 4 years ago

      Yes I’m confused on this

    • FRANI l 3 years ago

      Imo that works only if there is no coefficient before x. In the case you are talking about, we have 5x and 3x, which means that you have to check the answer by doing (5x*2)+(-6*3x)=10x-18x=-8x

  • peacefulman lian 4 years ago

    how did you write those on screen?

  • OVER FLY 4 years ago

    daym you hot

  • Maria Delgado 4 years ago

    Did u learn this in algebra

  • Andrea Tomasini 4 years ago

    you are too beautiful

  • Ahmet Miniksar 4 years ago

    I cant listen, when you on my eyes

    • Ayan Nur 3 years ago

      What does that mean pervert

  • unknown President 4 years ago

    I might need your help , Are you Avalible next Shark Week ?

  • 1twozero 4 years ago

    I’m smitten. Nancy, you do a great job explaining math.

  • Cyn rocks it 4 years ago

    Complex fractions / rational…omg please help!

  • abood 4 years ago

    Your videos have really become much more funny over the year. I like your humor.

  • Sami Daniel Montassir 4 years ago

    I love u nancy pi

  • Chatter's Box 4 years ago

    dude, if you time jump in the description, you dont put a period after. It wont detect any time jumps. just do 3:14 not 3:14

    (edit: totally kidding)

  • adam tesla 4 years ago

    Omg yr left hand like me but I’m idiot in math

  • Shalu singh 4 years ago


    • Shalu singh 4 years ago


    • Shalu singh 4 years ago


  • carolyngwright 4 years ago

    Sorry…the voice is annoying

  • David Ojumah 4 years ago

    she’s pretty

  • Bella C 4 years ago

    Brains and beauty. Your skin is beautiful Nancy

    • Big Weld 3 years ago

      Give me your skin

  • jason okoli 4 years ago

    you saved a life today

  • Xavier Xavier 4 years ago

    Glooks Shordy 💯

  • Gamebuster 12345 4 years ago

    Can’t get over the fact she’s writing backwards

  • Gabriel Galore 4 years ago

    please post more! you are a BIG help!!

  • Trade Viper Dave 4 years ago

    I want to know how you write backwards and why that doesn’t make you a spawn of the devil.

  • Dynamo Altis 4 years ago

    your voice is a medicine to all my daily problems.

  • Tis Is Simple Enough. 4 years ago

    All I really want to know is how you’re writing backwards like that..

    • Jay Khan 4 years ago

      @lord leoo actually its a glass with her writing but in editing she flips the video horizontally

    • Jay Khan 4 years ago

      if thats what u meant by mirrored then im totally just dazed lol

    • Crack Coder YT 3 years ago

      Bro she is using something called a light board. After recording the video she only flips the image so it looks like she is writing backwards

    • Ayan Nur 3 years ago

      She won’t tell u you dumbgirl

    • Usama rafieck 3 years ago

      Probably on a wall?

  • Jonathan An 4 years ago

    Jesus. Smart and beautiful. Marry me please?

  • Amarjeet Jatav 4 years ago

    I like your teaching ,,

  • Hadron Collider 4 years ago

    In calculus and up you have to define what set x is in, so might as well get into the habit writing the restrictions

  • Maths class KI 4 years ago

    Very useful video

  • Cassie Stewart 4 years ago

    I understand now woah

  • Tia Thathiah 4 years ago

    Hey Nancy, you really help a lot, great videos!!

  • Kedar Pravin Dhokarikar 4 years ago

    Nancy,, you look beautiful!!

  • Simón Caso 4 years ago

    Explicas muy bien. Gracias por tus videos !

  • Sam 4 years ago

    Absolutely love your explanations. I learned all this 65 years ago; you’re a great refresher and you fill in a lot I never heard.

    • KOT3Q 3 years ago

      How old r u and why were u watching this…respect

    • Eseel Alsammarraie 3 years ago

      @KOT3Q wow .. don’t think u should be asking … respect

    • KOT3Q 3 years ago

      @Eseel Alsammarraie fam im just interested into y someone would watch this after 65 years

    • Eseel Alsammarraie 3 years ago

      @KOT3Q yea yea , I gettit .lol . im curious too

    • W M 3 years ago

      KOT3Q That’s easy to answer. You see when you get older or more mature, it’s important to keep the brain 🧠 healthy. So good health is good diet, exercise, maths and lots of making out. So in a nutshell, keep on living like a 20 year old till you drop.

  • john fog 4 years ago

    Thanks this helped out now time to go show that final math exam who’s boss!

    • fatima a 4 years ago

      Good luck! Go get them As!

    • 100 subs without A single video 3 years ago

      john fog Covid 19 joins the chat

  • ARSHAN Soleymanian Far 4 years ago

    Marriage material

  • Robert Alvarez 4 years ago

    I been enjoying your math videos, a great refresher and I sm learning something new

  • Amirsalar Khodabandeh 4 years ago

    thank you so much, Nancy

  • Richard Cherry 4 years ago

    No need to feel disturbed by her classic beauty; Nancy is an outlier on the bell curve of normalcy…..a brilliant woman having a face that would qualify as a perfect model for a Renaissance artist like Rafael…she doesn’t know it, which enhances her appeal…IMO.

  • 너테기모함마드 마흐디 4 years ago

    Hello Nancy!
    how can we use Magic X for (10x^2 -7x -6)? while we can’t multiply 1 & -6 for -60 that becomes from a*c [in ax^2 + bx + c] and add -6 & 1 for -7 it becomes from b [in ax^2 + bx + c]
    I don’t undrestand :'(

  • Marec Huber 4 years ago

    Cant help wonder ? Depending on your answer ,if you have one,or respond, will become relative to me asking you another.
    What were your thoughts , if any, regarding the non cloning theorem for teleportation, when you first observed that the answer to the theorem was claimed to be hidden from human knowledge ?

  • Julia Morgan 4 years ago

    When she said “you don’t have to live like that”😂

  • THE UNKNOWN 320 4 years ago

    what a beautiful teacher,,

  • Ba A 4 years ago

    Sample #3…. what is the rule for inserting the -6 with the (5x ) instead of the +2 ? Which would have been (5x+2)(3x-6).

    • Leonardo Miguel 4 years ago

      Because developing (5x+2)(3x-6) the result is 15x^2-24x-12 which os different from 15x^2-8x-12 (original equation)

    • Ba A 4 years ago

      @Leonardo Miguel
      Perfect, got it…. thanks

  • Alexandra White 4 years ago

    ik this is really dumb but can anyone further explain the factoring portion of the third pproblem
    15x^2-8x-12 and how it factored to what Nancy got

    or at least link a vid to help my dumb self?

  • Mark Pineda 4 years ago

    Wow thank you . You made me forget I have a test on math

  • James Ashford 4 years ago

    You have my full attention, pretty and smart young lady! 🤓

    • Ayan Nur 3 years ago

      Ooh someone has a crush

  • David Mng 4 years ago

    No se como llegue aqui pero enseña muy bien la profesora

  • FiberHive 4 years ago

    My aunt is a math grad from MIT, unfortunately I live on the other side of the country from her. For now, it’ll be NancyPi to help with math while getting my computer science degree. SERIOUSLY thanks for this! Only thing is, it seems my book asks the trick questions and videos go over the simple rational expressions. I under stand these but for some reason it’s hard when i get something like 5/x-3

  • Saurabh Sethy 4 years ago

    Nice video. Hope to see more lectures.

  • Mountain Herb 4 years ago

    Nancy, you had me at ‘You don’t have to live like that.’ <3

    ETA: It's not true that x<>7 is required in Example 1 because there is not actually a singularity at x = 7. You know this (although a student at this level might not). Similarly with Examples 2 and 3. I think it’s true in general when you factor out a zero/zero binomial, as long as the surviving denominator doesn’t have a zero in the same place.

  • Enrique Alvizo 4 years ago


  • Chandra Babu 4 years ago

    U r explanation so good madam

  • vishal lakra 4 years ago

    you must write formula a^2 -b^2 = (a+b)(a-b)

  • Namal Indrajith 4 years ago

    Plese uf you can talk slowly , it difficult to understand non natives of english

  • Dinsmore Keir 4 years ago

    I love you Nancy

  • Shielyka Sumbrana 4 years ago


  • Paul 4 years ago

    You’re awesome!

  • Barlarkrishna Adhikari 4 years ago

    Thank you so much

  • Fahim M 4 years ago

    hey I love your videos are you still making videos there really helpful

  • Sean Thomson 4 years ago

    This was so helpful!!!! You are great! Thank you!

  • Le Alien 4 years ago

    “You’re like, i don’t know you tell me.”.
    Hahahahahahahaha. I love you Nancy.

  • Mylyn Camingawan 4 years ago

    Ilove vate mu expression

  • Reza Math Lessons 4 years ago

    could you graph the original function ?

  • BIKASH BANIK 4 years ago

    lol im in 6th grade and i understand all of this thanks to nancy

  • David Sewall 4 years ago

    Heat equation and diff eq?

  • Pouriya zeydi 3 years ago

    the third one has an oopsy in it … (-6+1 is not = to -7 ) its =–5 and ( -6+2 is -4 not -8 ) but any ways thanks for helping us ❤

    • Kemar Hamilton 3 years ago

      I knew I wasn’t going crazy and wasnt the only one who saw that.

    • EVRacer 3 years ago

      I was racking my brain how she got there lol.

  • Beatrice Castillo 3 years ago

    You are a heaven sent!!! Love your videos!!

  • Chayito C. 3 years ago


  • KOT3Q 3 years ago

    U r a god(ess) what my main land chinese teacher couldn’t do u did

  • roberto R 3 years ago

    I actually teach university math… and I still can’t stop watching her videos!

  • rcookman 3 years ago

    simple to simplify!!

  • Steve Nava 3 years ago

    What happend to the two?

  • Luis Fernando Tarazona Herrera 3 years ago

    I am sorry but in the last exercise you throw me out on the top simplification and the compositive quadrastic ….
    I know you make this exercises with your eyes closed, but please why there is a ÷6 and -2 ; if you added is -4 not ÷8

  • Kim Bryan Salo 3 years ago

    you did great for the explanation

  • Roger Lecloux 3 years ago

    Nancy can you tell us few words on your background? Very good videos. Tks

  • Diegos Drums 3 years ago

    I do not undrstand how she goes from 5x = 6 to x= 6/5?

    • LopsidedEdits 3 years ago

      She divided the x term and the 6 by 5 to allow a restriction to occur in simplest terms

    • Diegos Drums 3 years ago

      @LopsidedEdits Thanks 🤙

  • hassan hadi 3 years ago

    Thank you very much you helped me a lot.

  • jessica santala 3 years ago

    You explain this so much better then my teacher !! Thank you !

  • Inquire98 3 years ago

    “Thank GOD”, thank you very much ☺️ You are VERY good 😎

  • Ervin Siruno 3 years ago

    Hi! Do you have any videos on combination and permutation?

  • Skylar LacyBookworm 3 years ago

    This definitely helped. 😊

  • jade herrera 3 years ago

    You remind me of Lana Del Rey… lol. Thank you for this video!

    • Usama rafieck 3 years ago

      Whose that?

  • nidusaquilae76 3 years ago

    I chose the wrong major

  • M D 3 years ago

    10:40 ON THE TOP U CAN FACTOR 3….

    • Gustavo Nicasio 3 years ago

      You cant take 3 out of the 8

    • M D 3 years ago

      @Gustavo Nicasio yes you can, nancy tell him

  • gosnimm 3 years ago

    Isn’t the first problem x not equal to -7?

  • Abir Almoznino 3 years ago

    Can you post a video on multiplying, dividing, adding, and subtracting rational expressions!

  • Dilzar Bamerny 3 years ago

    Hi NancyPi, thanks for your videos. I need a sol. Of an eq.
    Could you find the value of X please in this eq. : sqrt(5-4x^2+8x)+sqrt(8x-4x^2)=9-8x+4x^2 .

  • Wardann 3 years ago

    Damn sexy

  • Michael Talmadge 3 years ago

    my favorite so far

  • Li 3 years ago

    WOW! She teaches this better then some teachers! 0.o

  • Dani cerul 3 years ago

    #nancypi you are the best, I understand every single video you upload. I have an A in math class because of you thank you! My teacher always complicates thing, and is not very clear.

  • Sheryl Atkinson 3 years ago

    Nanci Pi, MIT graduate, you’re smart and make Math beautiful just like you! You make math fun and doable. However, my son’s teacher will throw in exotic problems such as this: (2x-5)(x+3)/15-3x less or = 0. Where he has to graph the solution set and write it using interval notation. We have asked several people with our circle who are Math majors who get stumped because the haven’t had to do such problems in a long time.

    Teachers like the one my son has give Math a sour taste for kids who are already struggling. What is most frustrating to my son is that the teachers seems to work the easier problem in class on the board, but leave the more difficult ones for homework. Isn’t the goal to win kids to Math? Thank you in advance for helping to sweeten things up a bit for my son and so many others. 🙏 😃

    A concerned, yet hopeful mom who wants her kids to love Math like you do! 🥰🤗❤️

  • Heather Lee 3 years ago

    I usually watch all my youtube videos on x2 speed so when i put it on normal after watching one already sped up, I realized how seductive her voice sounds lol. Random. helpful video though!

  • abduljabbar mohammed 3 years ago

    Thanks a lot Nancy pie.You are a Brilliant brilliant tutor.

  • Dorian Taylor 3 years ago

    thank you!

  • Muhammad Roohallah 3 years ago

    Why are people so gross
    Please disable the comments…………………………

  • abdur raheem hosein 3 years ago

    Who else have engineering math exam tomorrow?

  • Jake Lopez 3 years ago

    Hey @nancypi, can you help my pass NES math304 test?

  • Jose Luna 3 years ago

    I am not confused anymore

  • Angel Morales 3 years ago

    Mire ha mi yo tengo halgo ke exponer sobre Hoyente ha distansia local interviene X X X cuantas mujer cuantas honbre (encuentro un misterio o paradoja univerasl y vamos ha Resolverlo cuanto antes mejor

  • mohammad ashraful 3 years ago

    I love u Nancy

  • mohammad ashraful 3 years ago

    I love you very much I want to be your friend

  • Spaced without a trace 3 years ago


  • otohns123 3 years ago

    Holy smokes

  • Robert Campbell 3 years ago

    Mathematically, this Is extremely simple. But what does it represent? This NancyPi could easily be a model. Beautiful.

  • Robert Campbell 3 years ago

    Math is one of the coolest inventions ever!

    • Ayan Nur 3 years ago

      Who gassed u up

  • Sultan khan jaffir 3 years ago

    very nice

  • Hayden Plays 3 years ago

    The reason I got into a selective school was 85% from these maths tutorials. Thank you so much!

  • James Lindgaard 3 years ago

    I hope this isn’t a Friday night (it is) but remembering stuff like this helps with the other stuff that comes later. You’ll still need to know it.

  • Ayan Nur 3 years ago

    I hate your voice

  • Hayden Wineera 3 years ago

    Bruh she has to write backwards on that clear board

  • Ryan McRae 3 years ago

    Nancy are you writing backwards or is there something else involved? Can you answer this question once and for all? lol also thanks great vid!

  • Shafe 3 years ago

    9:55 wholesome moment

  • Kame Senin 3 years ago

    We do not really “cancel the factor”. Rather we multiply by 1/(x-1) in the numerator and in the denominator. By doing that nothing changes since it comes back to multiplying by 1, if the denominator is different from 0.

  • Kame Senin 3 years ago

    Exercise 3, x cannot equal -1/2 neither.

  • Ricky Rick 3 years ago

    The ideal woman; beautiful and can teach me math.

  • James Grime 3 years ago

    Honestly, these video are brilliant.

  • Erik Garcia 3 years ago

    Can you please make a video on solving rational equations 😫🙏🏼

  • Skies 231 3 years ago

    This woman is smarter than me at my best.

    I’m not simping, no cap.

  • black arrow 3 years ago

    thank u .. for the video

  • Froggy Q 3 years ago

    Me to Nancy: Wanna hangout tonight?
    Nancy: 03:57

    • Ivy Bengtson 3 years ago

      YES!! That was good! I love it. Take a like from me.

  • Robert Dominguez 3 years ago

    Nancy, I’m with Grover on the last problem. -6 +2= -4 not -8?

  • Alisteire de Jesus 3 years ago

    thanks you Nancy!!!

  • Frank Thompson 3 years ago

    You are a great mathematician! You so fast at times it freaks me out! I’m older so I am just looking to re-fresh myself. You are an excellent teacher!!

  • mario marquez 3 years ago


  • Ramon Gonzalez 3 years ago

    your explanations are great !! I get the understanding ..thank you

  • Priscy Boafoah 3 years ago

    Love ur video

  • Augusta Yarteh 3 years ago

    Your explanation is great. The numerator is easy to factor. This how i will factor the numerator. Is (X+7)and (x_7) which is _49 For my denorminator. I will use. 2 and negative _ 7 and so forth to solve the denominator. My own short distance to solve that expression. Thank you my dear Nancy. Can you make video to work on. trynomo please. Your explanation is great trust me.

  • Dynamic Ki 3 years ago

    She look like a famous model

  • Zedsu'sRevenge 3 years ago

    from heaven above

  • I’m not telling you who I am 3 years ago

    Ahh thank u! This helped A LOT 🙂

  • Noman Shah 3 years ago

    hey nancy i failed 5 times in math i dont know why i watched every single video of your classes any ways now im studying arts love your classes still

  • Bill Wilphenton Jean Toussaint 3 years ago

    Nancy, you are the best. because of you, I got P for my math class.

  • Jasper Sharp 3 years ago

    im so confused

  • Vilayat Ali 3 years ago

    Nancy gorgeous maths teacher

  • Tana Roj 3 years ago

    i just noticed shes writing backwards… damn thats talent

  • Mark Wadsworth 3 years ago

    I assume you are right handed and flip the video left right? Great sound effects!

  • Alexandra Kaidan 3 years ago

    Cancel a can?

  • Bob Beattie 3 years ago

    That was very useful.

  • steven lodge 3 years ago

    I don’t get what you do with -8 please

  • Mister ListerField 3 years ago

    Can you do a video on adding and multiplying rational expressions?

  • Heriberto Gutierrez 3 years ago

    Gracias por la información de la reducción buen método

  • matar mbe 3 years ago

    so sweet

  • matar mbe 3 years ago

    and pretty

  • Ogle Noelle 3 years ago

    0:22 oooo I think I heard some Nancy humor in there

  • Sushil Khatri 3 years ago

    Nancy in equation no. 3 how that -6+2=-8 ?

  • Gay Bois 3 years ago

    She has such a nice voice

  • MEЯLIИ 3 years ago

    Is having ure hears rightside a symbol for an obsessed clan/cult? Ouh goddamn u got busted by me. I am gonna send u an swat.

  • Maribel Gonzalez 3 years ago

    I’m gonna cry I’m so lost

  • joed596 3 years ago

    Can’t do calculus until you learn these concepts thoroughly 🙂 Thanks & thumbs up 👍

  • ibraahim ahmed 3 years ago

    Slow down with the instructions because am using a computer too just letting you know smart lady love ur video with passion

  • Alessandro Squeo 3 years ago

    Great video. How do you record the transparent transparent board. Can you describe your video setup. I’m an instructor myself and I would like to implement a similar method for my students in CIS

  • Chelsea O 3 years ago

    I’m not even in school anymore I just love watching her videos for fun 😌

  • Yash Pal Goyal 3 years ago

    0:58 yeeeeeesss, please show me for the complicated cases of functional equations. it seem like rote learning the existing methods to me. I cant quite get my head around it.

  • Average_ TTV 3 years ago

    “If you’re one of the wise ones you’ll stick around.”

    Me that’s definitely not wise but definitely still needs to stick around

  • Rosie N 3 years ago

    I have a question please I need help with it
    if y=2×4 and h=4x+6 fine a and y

    please can someone help me please please please

  • ꧁༒ⱤɨCʞƔ༒꧂ 3 years ago

    wow you’re damn hot

  • Wade Deadpool 3 years ago

    hey i have been wacthing your videos i really recommend you to solve a jee mathamatics paper

  • ertas zorlu 3 years ago

    You are beautiful NancyPie

  • Lizzy jka 3 years ago

    This video made me understand something that no teacher could

  • Jojo Davis 3 years ago

    you’re hilarious but i finally get it. thank you

Comments are closed.