Simplifying Rational Expressions... How? (NancyPi)

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 kzbin.info/www/bejne/j6WxapKqeMaFh8U
For how to FIND the DOMAIN of a function, jump to kzbin.info/www/bejne/fYKqd4CLm9dkZq8
For more factoring examples in my video on how to solve quadratic equations by FACTORING, jump to: kzbin.info/www/bejne/kGawn4NvmcZne68
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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 kzbin.info/www/bejne/p3vVo42HnLiehZo
For more math help and videos, check out: nancypi.com
Edited by Miriam Nielsen of zentouro: kzbin.info

[@sam9242]

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.

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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

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

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

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Jerry's Studio agreed!

[@elioraa.6586]

Thank you for showing how you did the factoring! My teachers just skip over those details, and I have trouble factoring, and this helps me remember how to do it with different types of equations. Thanks!! These math videos are helping so much!

[@TheZooman22]

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.

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

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I actually plugged it in and saw it from that bit and that was funny

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

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

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

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

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

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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

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

[@Playgrl966]

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!!

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Shitiest job

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

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You've been a great inspiration to me Nancy, my mentor. Wanna be a great mathematician like you 😊.

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All I can think about is how she is writing backward for our benefit, since she's standing behind a clear writing surface

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Honestly, these video are brilliant.

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I don't know why there's about 2% who disliked this tutorial. I find this tutorial very very good. Thanks NancyPi for making videos like this.

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I love Nancy Pi. Thanks for all the great videos

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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!!

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You are one of my best Math teacher. Thanks a lot Nancypi

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Always a relief to be able to pause, rewind and watch many times a video; instead of a real time class 🙄

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

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@@askhfbfns67589 stop SAYING bad words UR SO DISRESPECTFUL THIS IS WHAT YOU COMMENT AFTER WHAT JALBRIS SAID THAT STOP ASKING QUESTIONS WITH BAD WORDS. PLEASE :(

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"You're like, i don't know you tell me.". Hahahahahahahaha. I love you Nancy.

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You saved my life. You've taught me like 5 things today.

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your videos are amazing, they help me A LOT

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

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can you do a series of SAT Math problems.

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

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Thank you for putting this out there, very helpful

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

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please post more! you are a BIG help!!

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it’s always nice to listen to a beautiful math teacher

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Love the way this is explained along with the jokes. Definitely makes math more entertaining. Keep it up!

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

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You outdid yourself today....thanks very much.

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Very use full Nancy ...👍👍❤

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Thanks for this vid. I need more practice in this. I'm subscribing now, as I'm finally getting back to my math after a long hiatus, and I really need to shake the rust off of my mathematical techniques.

[@ramongonzalez4042]

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

[@NigelDAllen]

Excellent instruction! And hilarious...thank you Nancy!

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

[@anthonybanks4958]

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!

[@Salehalanazi-7]

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

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Explicas muy bien. Gracias por tus videos !

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

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

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

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

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

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

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

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Literally life saver i was very close to dropping the class

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Wow - Thank you! I love your videos

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you are my favorite maths teacher

[@justinr3226]

Oh my god I think the only reason I’m going to pass my precalc is because of these videos. You explain it very well, and with little humor breaks it keeps me paying attention. Thanks!

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

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Thanks for knowledge Nancy it really helped me 😙😙👍👍👍

[@stefanovankellytrazzi2686]

You are a fairy 🧚‍♀️ bringing education in my quarantine. Thank you so much for your time and dedication, you are the best.

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

[@TheManWhoDraws]

very helpful, thx Nancy

[@amirsalarkhodabandeh9916]

thank you so much, Nancy

[@maller91]

Great! More videos like this!

[@peterpzazz2441]

Hi Nancy. Your math knowledge is impressive. I hope this knowledge led to an amazing career for you.

[@rebeccaamodeo7901]

Thanks for helping prevent summer slide on my math skills!

[@MathsclassKI]

Good

[@MathsclassKI]

Good

[@abduljabbarmohammed4188]

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

[@airheadish]

my favorite so far

[@donaldmrambojr5695]

These video's help very much. ALL of this stuff are my favorites and lots of fun to play with. I still love math, even in my 60s. Love the video's, NancyPi!!! Thank you for re-kindling my interest in this always fun and fascinating subject!!! As NancyPi says, "Like & subscribe"!!! Highly recommended!!!

[@starmanmcfly2752]

Why do we not have to add our 2 factors to equal the middle term? The last simplification does not equal to -8x or -7x....first she says that we need to find two numbers that multiply that also add together to equal to the middle term...then in the last rational expression all we do is multiply and ignore that the two multiples do not add together to make the middle terms anymore...I am really confused and it hard to type out, but please anyone help me....we have (3x-6)(5x+2) which multiply to -12 but do not add to -8. What did I miss? please help!????!!

[@saurabhsethy2937]

Nice video. Hope to see more lectures.

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Big fan of your work!

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

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thanks you Nancy!!!

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

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You deserves more views.

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You are a great teacher

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“I know you think you’re slick”. Wow Nancy I feel called out

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Ikr lmao 😭

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great smart sharing your videos, thanks!

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Thank you for the help 😊

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Thank you so much!

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"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

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you did great for the explanation

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Thank you very much you helped me a lot.

[@XxMesmerized1LOvEXx]

thank you so much you're a great teacher!

[@usamarafieck1715]

She makes it easy to understand for me.

[@DanielWalker.]

She writes better backwards than I do fowards! Plus she's a freakin angel...

[@adrianoianase]

I don't think she writes backwards... it's easier to just invert the video

[@didactichub478]

Thanks A Bunch 🙂