06 - Simplifying Rational Expressions in Algebra, Part 1

View more at www.MathTutorDVD.com.
In this lesson, you will learn what a rational expression is in algebra and how to simplify rational expressions. A rational expression is any expression that can be written as a ratio of two polynomials.
In a similar way, a rational number can be written as a fraction with numerator and denominator, a rational expression can be written with a numerator that is a polynomial and a denominator that is also a polynomial.
Here we focus on how to simplify these types of expressions, which usually involves factoring the numerator and denominator and canceling common terms.

Пікірлер: 107

  • @firetalongames91
    @firetalongames913 жыл бұрын

    I'm in algebra 2 and my teacher doesn't explain any of this. He shows us him doing a problem and then we're given an assignment. Watching these videos are such a big help.

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @chinmaibommana9788

    @chinmaibommana9788

    2 жыл бұрын

    Wait, this is in algebra 2?

  • @firetalongames91

    @firetalongames91

    2 жыл бұрын

    @@chinmaibommana9788 for me it was. Idk how it will be for you. If it is, good luck

  • @chinmaibommana9788

    @chinmaibommana9788

    2 жыл бұрын

    @@firetalongames91 oh thank you

  • @tomjoad6993
    @tomjoad69934 жыл бұрын

    12:15 I just now realized what factoring really is and what it can be used for. Factoring is rewriting a number or expression so that it is the product of multiplication. And one reason for doing this is so you can cancel out terms in a fraction in order to quickly simplify it. You cannot cancel common terms between the numerator and denominator if there is addition or subtraction involved between any of the terms, so factoring it makes everything the product of multiplication instead of addition / subtraction, which then allows you to cancel terms. I really love when things start coming together and everything becomes clearer.

  • @tomjoad6993

    @tomjoad6993

    4 жыл бұрын

    When I first started learning Algebra, which was only about a week ago. This is the first question I asked when something didn't make sense to me: "I was watching a video that says 9x + 3 / 12x + 4 can be simplified to 3/4. But can't just 9x / 12x be simplified to 3/4? Can't 9x + 3 / 12x + 3 also be simplified to 3/4? How can they all be the same thing when they are clearly not the same thing? I understand how 9x / 12x and 9x + 3 / 12x + 4 are the same thing. But what about 9x + 3 / 12x + 3? Isn't that also 3/4? Since don't the + 3's on each one cancel each other out? " Do you see at the end where I said, "Don't the 3's cancel out?" And they don't because they are being added to the other terms not multiplied.

  • @tomjoad6993

    @tomjoad6993

    4 жыл бұрын

    Something else I just realized, too. When you flip terms that are being added or subtracted by multiplying by -1 you are simply factoring it! I was wondering where you get the -1 from. But all you are doing is finding a way to make it the product of multiplication. It's like taking a single number 12 and rewriting it as 3(4). Where did you get the 3 and 4 from? You simply made 12 the product of multiplication by using its factors! THAT'S WHY THEY CALL IT FACTORING, JASON! I HOPE YOU LEARNED SOMETHING NEW TODAY. :)

  • @mar617
    @mar6173 жыл бұрын

    DUDE YOU LITERALLY SAVED MY LIFE I AM FR SO SO SO GRATEFUL THANK YOU THANK YOU THANK YOU THANK YOUUUUUUU

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @clarencewilliams8953

    @clarencewilliams8953

    3 жыл бұрын

    @@mathfullyexplained aAAa!!a

  • @georgeh1352
    @georgeh13523 жыл бұрын

    Neat trick using ( -1), wish I had been taught that at school/college. Pot luck on the quality of Teacher / Lecturer you get, thanks for your clear and top notch explanations.

  • @juniewindsor-ji7gg
    @juniewindsor-ji7gg5 ай бұрын

    I just want to thank you for your series, as a senior going back to school to get my grade11; 12 algebra, you,ve been a blessing, as on line books don't explain anything. I found you late in my grade 11 class, happy to say I passed not the mark I wanted but it's still a pass and I continue with you in grade 12. these classes are fast 2 years into 1, talking about math I never knew existed could not relate until I started watching you. Again thank you sooooo much, I am sure many others appreciate your dedication, time and knowledge to help others 😊 thank you 👏👏👏👏

  • @Jessicanimation
    @Jessicanimation Жыл бұрын

    With limited time in the classrooms and our instructor can only show us so much. God bless KZread.

  • @blaneferris9952
    @blaneferris99522 жыл бұрын

    It's helps so much that you rewrite the problem before cancelling, other videos look so complicated when they do it all on top of the original problem.

  • @marianusStaff
    @marianusStaff5 жыл бұрын

    Thank you for all the time you spend for this lessons!

  • @MathAndScience

    @MathAndScience

    5 жыл бұрын

    You are very welcome! View all my Lessons and Courses! Visit: www.MathTutorDVD.com

  • @exotickhanaarif4333
    @exotickhanaarif43332 жыл бұрын

    Wow man that -1 is such an important tool it helped me understand what Factoring really is

  • @patrickvanbramer5318
    @patrickvanbramer53183 жыл бұрын

    My son's teacher just keeps piling on the homework, but many kids dont understand fully, including himself. Makes no sense. My son said you're better at teacher than his teacher. Thankyou

  • @PalenVencatachellum-xo3fc
    @PalenVencatachellum-xo3fc Жыл бұрын

    I thank you very much for your explanation which is very simple to assimilate by anybody.

  • @dusannovakovic5257
    @dusannovakovic52574 жыл бұрын

    Great lecture. If only there were more professors like you, especially for math and sciences. There is an interesting point I never thought of until now. Maybe you could've used the example with s^2-t^2/(s-t)^2 to show explicitly that (s-t)^2=(t-s)^2 which is pretty convenient to keep in mind when solving similar equations because such manipulation makes the process faster.

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @sonnyl2915
    @sonnyl29153 жыл бұрын

    The only teacher could explain maths!👍

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @KDA1342
    @KDA13425 жыл бұрын

    Thank you for all that you do!

  • @thedoctordowho2022
    @thedoctordowho20224 жыл бұрын

    Thank very much for you time to do this lessons.thank you!!!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @mathbbn2676
    @mathbbn26762 жыл бұрын

    Very good teacher, I can understand your presentation on this lesson. This radical equation is I know that this teaching makes students understand and thank you teacher

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    Awww thanks so much.

  • @mathbbn2676

    @mathbbn2676

    2 жыл бұрын

    @@MathAndScience yes teacher

  • @haleymills239
    @haleymills2392 жыл бұрын

    Just a question but I was told you minus exponents when dividing. So why instead of x/x^2 do you not get -x and have to move it up?

  • @davidhunter4945
    @davidhunter49456 ай бұрын

    Superb class. Taught me so much, thank you.

  • @smitachaudhary9519
    @smitachaudhary95193 жыл бұрын

    It was useful session :)! I like the sessions from Vidya Guru channel as well. Their important questions were proven very helpful in my SSC exam.

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @masterhalim8263
    @masterhalim8263 Жыл бұрын

    neat writing and clear explanation. i like it

  • @shaboog2644
    @shaboog26442 жыл бұрын

    Where can I buy his full videos??

  • @MathAndScience

    @MathAndScience

    2 жыл бұрын

    Visit www.MathAndScience.com. Thanks so much!

  • @dengex2260
    @dengex22603 жыл бұрын

    great video, I like the way you teach!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @yesserlabidi7831
    @yesserlabidi78314 жыл бұрын

    you are the best teacher i have never saw !

  • @MathAndScience

    @MathAndScience

    4 жыл бұрын

    Wow thank you!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @Sixtoe981
    @Sixtoe9814 жыл бұрын

    You my man are on fire! Your teaching is superb.

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @English-ug2cs
    @English-ug2cs3 жыл бұрын

    Excellent greetings Mr Jason

  • @qusaialhariri8117
    @qusaialhariri81174 жыл бұрын

    your explanation is really amazing and I actually have learned a lot from that lesson. Thanks a lot sir and keep it up

  • @MathAndScience

    @MathAndScience

    4 жыл бұрын

    You are very welcome!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @jasminparveenparveen7061
    @jasminparveenparveen70615 жыл бұрын

    You explain very well sir 👌👌

  • @MathAndScience

    @MathAndScience

    5 жыл бұрын

    I really appreciate it! View all my Lessons and Courses! Visit: www.MathTutorDVD.com

  • @markfinn825
    @markfinn8253 жыл бұрын

    Some numbers with decimal points can not be written as fractions . But if the circumference of perfect circles are divided by their exact diameter is the number always the same ( no matter what the size of the circle ).

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @HuongPham-gy5nh
    @HuongPham-gy5nh2 жыл бұрын

    Very good and funny videos bring a great sense of entertainment!

  • @chimamandaogbuagu7227
    @chimamandaogbuagu7227 Жыл бұрын

    Thanks you very much it really helped

  • @KalkidanYitayew
    @KalkidanYitayew8 ай бұрын

    Thank you 🙏

  • @guillermaalberina7648
    @guillermaalberina7648 Жыл бұрын

    Thank you very much

  • @molokoplus4544
    @molokoplus45444 жыл бұрын

    You're the best math teacher ❤

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @leslielangaylangay9295
    @leslielangaylangay92953 жыл бұрын

    Thank you for this lesson Sir

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @mr.stranger3417
    @mr.stranger34173 ай бұрын

    Thank you sir ❤

  • @jonwill
    @jonwill6 күн бұрын

    Jason, (or anyone) On the problem just before the last 31:08 with the result: x-2/x-4, why wouldn't you further factor x-4 as a difference of squares? Factoring as: (√x+2)(√x-2). Is there rationale for no longer factoring when factoring further is possible? In general does one stop factoring when no cancellations will result? Any insight is appreciated.

  • @gtlasers1

    @gtlasers1

    5 күн бұрын

    factoring further when no cancellations are possible isn't needed for simplifying rational expressions. Once you've factored to the point where no further simplifications or cancellations can occur, you've done enough and none else is needed. The expression x-2/x-4 does not have any common factors to cancel out, so it's considered fully simplified. Factoring x−4 into √ ( 𝑥 + 2 ) √ ( x ​ +2) wouldn't help because it isn't a good factorization for non-perfect square X. In summary, additional factoring is not required if it doesn't lead to cancellations or simplifications of the origin equation.

  • @jonwill

    @jonwill

    4 күн бұрын

    @@gtlasers1 Thank you for helping me understand why Jason stopped factoring, and the general rule for when to stop. I much appreciate your input.

  • @malissawhite3735
    @malissawhite37352 жыл бұрын

    You rock! ☺️❤️

  • @rickdeckard2622
    @rickdeckard26223 жыл бұрын

    Best teacher on KZread!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @rickdeckard2622

    @rickdeckard2622

    3 жыл бұрын

    @@mathfullyexplained Give me pls the link. I didn't find it.

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    @@rickdeckard2622 type mathfullyexplained one word

  • @3aliushiaboaziz983
    @3aliushiaboaziz9833 жыл бұрын

    Thank you verry much sir

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @evangilistbarnes
    @evangilistbarnes2 жыл бұрын

    Hi John, I have to take the middle school praxis. Do you have and suggestions for me to be successful and pass?

  • @kevinrivera880
    @kevinrivera8802 жыл бұрын

    THis guy is a beast.

  • @yesserlabidi7831
    @yesserlabidi78314 жыл бұрын

    thankss !!!!!!!!!

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @dailycraft5855
    @dailycraft58553 жыл бұрын

    Thanks

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @aganachris7058
    @aganachris70582 жыл бұрын

    You're good

  • @eslamelsofany2470
    @eslamelsofany24705 жыл бұрын

    Please sir reply on my question Are you intend to make series for electrical machines and power systems in the future or not ?

  • @crisjelasio5221
    @crisjelasio52212 жыл бұрын

    Ty

  • @vienbenz3646
    @vienbenz36464 жыл бұрын

    Thank you sir

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @saschaveloso6369
    @saschaveloso63692 жыл бұрын

    Godbless you sir

  • @b.p.sadashivamurthy2575
    @b.p.sadashivamurthy25754 жыл бұрын

    Hello sir, I have found the five rational numbers between 1 and 2 using equivalent fraction. The five rational numbers are - 7/6 , 8/6 , 9/6, 10/6 , 11/6. Sir, is it compulsory that we should simplify the above five rational numbers. Please help me with the above doubt. Thank you.

  • @richardbrookens2896

    @richardbrookens2896

    2 жыл бұрын

    7/6, 4/3, 3/2, 5/3, 11/6

  • @SohailKhan-le5rj
    @SohailKhan-le5rj5 жыл бұрын

    Good sir

  • @MathAndScience

    @MathAndScience

    5 жыл бұрын

    So happy you liked it! View all my Lessons and Courses! Visit: www.MathTutorDVD.com

  • @alaa-xw1jz
    @alaa-xw1jz11 ай бұрын

    what the lesson I have to get before this lesson. I want to understand basic before this one

  • @tz8565
    @tz8565Ай бұрын

    9:10 26:12

  • @willbe9326
    @willbe93263 жыл бұрын

    I need to listen to my teacher for 3 hour to get lesson but for you 30min thank you so much

  • @mathfullyexplained

    @mathfullyexplained

    3 жыл бұрын

    Try my channel mathfullyexplained. Full unit on rational expressions plus more units

  • @castilloralphangeloa8392
    @castilloralphangeloa83922 жыл бұрын

    Hello there, excuse me sir, do u have an video tutorial about partial fraction decomposition

  • @shawnouellette1953
    @shawnouellette19537 ай бұрын

    Why can't you multiply and divide irrational expressions perfectly?

  • @AshutoshYadav-mf8mv
    @AshutoshYadav-mf8mv Жыл бұрын

    An

  • @laurenschubert161
    @laurenschubert1613 жыл бұрын

    My teacher does a very easy problem then the next one is very hard

  • @DicsionHlordze-tv2xx
    @DicsionHlordze-tv2xx Жыл бұрын

    Please don't you teach chemistry?

  • @johnsmapreacher6525
    @johnsmapreacher65252 жыл бұрын

    Down in the weed. I'm getting english lessons on idioms.

  • @MM-dj2cv
    @MM-dj2cv2 жыл бұрын

    BUT WHY DONT YOU LIKE USING SHORT CUT.

  • @homosapien.a6364
    @homosapien.a63642 жыл бұрын

    i thought i was dumb but it turns out that my teacher don't know how to explain it 😭😭💔

  • @chrissystewart6268
    @chrissystewart6268 Жыл бұрын

    Ready to reverse before I take my GED 2023 I accept to earn my High school diploma

  • @abhishekshukla7052
    @abhishekshukla70523 жыл бұрын

    Bakwas

  • @annieracelis9020
    @annieracelis90202 жыл бұрын

    Math is bad for your health

  • @rhoddustine2491
    @rhoddustine24915 жыл бұрын

    F*ck this math.

  • @vixyvelasquez9898
    @vixyvelasquez98987 ай бұрын

    Is this part of algebra 1 or 2 ?