❖ Partial Fraction Decomposition - Repeated Linear Factor ❖

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  • Опубликовано: 18 янв 2025

Комментарии • 257

  • @amenff2626
    @amenff2626 13 лет назад +29

    Patrick, u definitely did better job than any one of my lecturers. U saved my math subject. Praise for your generosity in teaching.

  • @RGBY-tv4hg
    @RGBY-tv4hg 4 года назад +144

    Almost 10 years old but this is still incredibly helpful, thanks

    • @adude8883
      @adude8883 3 года назад +2

      True

    • @hectorgomezyanez6327
      @hectorgomezyanez6327 3 года назад +13

      @@adude8883 Is not question of time, remeber you are learnig mathematics from egyptians.

    • @PastaSenpai
      @PastaSenpai 2 года назад

      @@hectorgomezyanez6327 bruh what

    • @Do-Some-Change
      @Do-Some-Change 2 года назад +1

      Now I'm 16 now it's helpful to me

    • @hillkid2755
      @hillkid2755 2 года назад

      And now it's been 2 years since you posted that comment.

  • @patrickjmt
    @patrickjmt  4 месяца назад +4

    Hi all! Wanna help a RUclips education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)

  • @perushank
    @perushank Год назад +5

    Helped me get through Calc 2 four years ago, and now helped me figure out how to find the derivative of the sigmoid function for a graduate course. I hope future generations find patrickJMT's awesome videos!

  • @juanmse
    @juanmse 12 лет назад +15

    I was so confused my teacher was leaving out so many steps. Thank you so much.

    • @ID_Station
      @ID_Station 3 года назад +1

      They literally skip the entire system of equations part and just write the answer. Here I am thinking this is gonna take 5 minutes to do lol

  • @raulh5008
    @raulh5008 8 лет назад +11

    This is when matrices and row reducing saves a lot of time! Excellent video, thank you!

  • @patrickjmt
    @patrickjmt  13 лет назад +7

    @crystalakajuicy very happy that i could help : )

  • @sardina1995
    @sardina1995 10 лет назад +6

    Thank you so much PATRICKJMT !!!! you are like the go to youtuber known in my campus, highly recommended by my peers mathematics&engineering majors. It would SO MUCH FUN, if you include trig partial fraction exercises !!!

  • @byrnejobie
    @byrnejobie 8 лет назад +9

    patrickJMT is dareal MVP

  • @yoporock
    @yoporock 13 лет назад +4

    Thank you so much!, you have no idea how helpful that was; you make it so easy to understand :')

  • @jesschappellable
    @jesschappellable 11 лет назад +13

    Thanks for your videos! I use your channel the most when doing calculus homework.

    • @patrickjmt
      @patrickjmt  11 лет назад +11

      you are welcome and thanks for watching! i appreciate it

  • @ducksoop.x
    @ducksoop.x 7 лет назад +9

    I finally get it. Thank you, you are a godsend. Hope I can pass the second exam!

  • @yenfong2564
    @yenfong2564 9 месяцев назад +1

    Best vid on explaining partial fraction! HIghly Recommended.

  • @Pk.Comment_on
    @Pk.Comment_on 7 месяцев назад +1

    Thank bro I am clearly understand now

  • @blkteg21
    @blkteg21 14 лет назад

    Your the best Patrick. Nothing but praise for you.

  • @eddyflako8959
    @eddyflako8959 9 лет назад +26

    Thats sarcastic joke at the end tho

  • @khalil4509
    @khalil4509 3 года назад +2

    Let’s go pre-calc students!

  • @olubukolaogunsola5864
    @olubukolaogunsola5864 6 лет назад

    I wonder what the guys that don't like this video want. Excellent and free resource . Thank a lot

  • @lolochan6645
    @lolochan6645 9 лет назад +3

    Thank you very much :3 I always look for your videos when I have an exam and want to understand well
    Good work keep going ^^

  • @maxxz_7033
    @maxxz_7033 2 года назад +4

    Who watching this one 2022 😀

  • @TheEazyDuzIt95
    @TheEazyDuzIt95 14 лет назад +4

    Why is B's denominator (x+3) and C's denominator (x+3) squared? Shouldn't C's denominator be (x+3) as well?

  • @shaheerjan1336
    @shaheerjan1336 Год назад

    Thanks! This video was so helpful I recommend it to all people .Thanks once again .

  • @ID_Station
    @ID_Station 3 года назад +1

    Damn! Thank you for this. Talking Calc 2 and we are at the point where no one does the steps anymore. We go from problem to answer lol

  • @shmiddy8
    @shmiddy8 13 лет назад +1

    @TheEazyDuzIt95 I agree. I think that C's denominator has to be (x+3)

  • @thetruth6781
    @thetruth6781 3 года назад

    Man, you deserve all the best. Damn you did a great job with it. 😍😍👍

  • @Dvno92
    @Dvno92 12 лет назад

    YOU ARE A GENIUS!!!!!! Thank you so much! GOD BLESS YOU!!!!!!

  • @jaalle-11
    @jaalle-11 8 лет назад

    Thank you man! You're a great teacher.

  • @salmitchitumba8314
    @salmitchitumba8314 7 лет назад

    I'm really thankful for the videos.... They help a lot

  • @vladradoi
    @vladradoi 12 лет назад

    found this 7 days before my final exam,just wanted to say thanks !

  • @lwisamutale9239
    @lwisamutale9239 2 года назад

    Well explained sir🙏
    2022 first year student has benefited from your video 👏

  • @IamJacksColon4
    @IamJacksColon4 8 лет назад +7

    u didnt explain why B only has x+3 as a divider and C has x+2 ^2 divider. this is the most important part of the whole thing!!!

    • @harshmk1052
      @harshmk1052 5 лет назад +1

      can someone explain me this point please ?
      It will be a great help :)

    • @Luke-kq8gh
      @Luke-kq8gh 5 лет назад

      Harsh mk I’m learning too and I have my midterm on Friday. I think you just have to memorize this step. As the exponents build up so (...)^3 would need three fractions?

    • @tylerh31444
      @tylerh31444 4 года назад +2

      3 years later and I need to know this answer to this questionnnn. not explained in my textbook or any video I've seen about these problems.

    • @rekhabijupal6237
      @rekhabijupal6237 4 года назад

      Basically he has taken the LCM of (x+2)^2 which is equal to (x+2)(x+2)^2
      And if ur asking why is that only (x+2) is B's divider and (x+2)^2 is C's divider, take it as a common rule to apply here.

  • @hrishishirke5461
    @hrishishirke5461 2 года назад

    12 years, and still helpful

  • @axpence
    @axpence 12 лет назад +1

    Whenever you factor out the denominator as much as possible and you are left with (x+3)^2 , when doing the partial fraction decompision you have to BUILD YOUR WAY UP to the power. So let's assume that you factored out as much as possible and ended up with a denominator of (x+3)^26. You would have to build up to the 26th power by doing a/(x+3)^1 + b/(x+3)^2 ... z/(x+3)^26

  • @ruhamdaniel3082
    @ruhamdaniel3082 2 года назад +1

    tnx tnx a lot you are seen the main point for me 😊

  • @arnelnamoc504
    @arnelnamoc504 9 лет назад +8

    just want to ask what happened in the denominator of B AND C,why there is still an exponent of 2 in the C where its factor is just (x + 3)(x+3)

    • @tacticalultimatum
      @tacticalultimatum 8 лет назад

      It's right but I don't know why

    • @sullivanmaclellan4798
      @sullivanmaclellan4798 7 лет назад

      That's what trips me up too

    • @zip9267
      @zip9267 6 лет назад +3

      The reason for this is because when you're multiplying out the (x+1)(x+3)^2 to the right side, you need to cancel out (x+3)^2 for the C term, thats why C is only C(x+1) and not C(x+1)(x+3)^-1

    • @irekoyaaishat3344
      @irekoyaaishat3344 6 лет назад

      Arnel Namoc H

    • @aqeelmurtaza5561
      @aqeelmurtaza5561 6 лет назад

      Yah u r write

  • @thomasgomez3284
    @thomasgomez3284 9 лет назад

    omg thank you so much patrick i owe you my life definitely worth that sub man keep doing what you're doing you helped me sooooooo much

  • @engineerbrian7935
    @engineerbrian7935 Год назад

    Thanks alot.... May the almighty God bless you 🙏🙏🙏🙏

  • @witneyh9353
    @witneyh9353 8 лет назад +13

    welll that escalated quickly.

  • @evanmargolis8468
    @evanmargolis8468 9 лет назад +2

    I got A=-3/2, B=-2, and C=1 . I used your guess and check method to make x = -1, and x= -3 in order to cancel out some of the problem and find c and a easily.

  • @helmyfarhan
    @helmyfarhan 8 лет назад

    thanks a lot patrick, i feel better with this topic now, now i got new easy way to solve this question thanks again patrick really help me

  • @itsjustinn146
    @itsjustinn146 5 лет назад

    Is that foiling at 3:41?

  • @monkeyninjas8
    @monkeyninjas8 13 лет назад

    OH MY GOSH THANK YOU!!! i'm in 9th grade and my parents don't get this, my teacher doesnt explain it well at all, and my classmates are all nerds so they can't explain it well at all haha...
    THANK YOU SO MUCH!!! :D

  • @rahulteja1858
    @rahulteja1858 2 года назад

    Thanks alot man as they say old is gold

  • @corn1jacob
    @corn1jacob 11 лет назад +1

    Why do you have to build your way up to the power I can take it as a rule but do you know why that is so?

  • @anikid123
    @anikid123 10 лет назад +7

    why do we have to use (x+3)^2 for C? why is it to the power of 2 but not 1??

    • @nounisirinaa6461
      @nounisirinaa6461 6 лет назад

      @RUNESCAPEISLIFE S still didn't get it can you clarify please😯😯

  • @OSMADO
    @OSMADO 6 лет назад

    Even after 4 years, currently a senior, I come back to this video to review knowledge that I had forgot.

  • @jahansaid6382
    @jahansaid6382 8 лет назад

    Thank you very much, I love the way you explain things. So far after khan academy I found you the best, I understand you say:)

  • @sowmy_01
    @sowmy_01 Год назад

    Thanks a lot, It's very helpful!!

  • @aku7598
    @aku7598 Год назад +1

    Why not just first substitute x=-1 eliminating B and C
    Then x==-3 eliminating A and B.

  • @sowm_01
    @sowm_01 10 месяцев назад

    Thanks, it's truly helpful!

  • @lifelonglearner8794
    @lifelonglearner8794 8 лет назад +2

    simple but complete
    ALLAH bless u my teacher!

  • @danielnegussie4894
    @danielnegussie4894 18 дней назад

    very good lesson, thank you.

  • @randomositalica
    @randomositalica 12 лет назад +3

    "The left side is just hangin out." Haha

  • @naa-ilahdaniels9848
    @naa-ilahdaniels9848 10 лет назад

    Awesome vid! Helped me so much with my test :)

  • @marcjasondelossantos8120
    @marcjasondelossantos8120 10 лет назад

    Thank you soooo much man,this will surely help me with my quiz nextweek

  • @saadmuzamil9891
    @saadmuzamil9891 4 года назад

    Thanks for this video this was very helpful in exams

  • @arjunraj8717
    @arjunraj8717 3 года назад

    Well explained dude❤️❤️

  • @rishijain6465
    @rishijain6465 8 лет назад

    At 7:00 you might have subtracted the 2nd and 3rd equation, and then solve for 1st equation and the result. It would be much simple.

  • @thebiharangirl4636
    @thebiharangirl4636 4 года назад +1

    Thank u very much
    Ur explanation is just woooooo

  • @axpence
    @axpence 12 лет назад

    THANKS PATRICK!

  • @abed.al-sqoor4598
    @abed.al-sqoor4598 9 лет назад

    thanks a lot Patrick you're amazing

  • @shannieahluna5206
    @shannieahluna5206 Год назад

    "What were you doing on Halloween?"
    This guy:

  • @jannathussain6987
    @jannathussain6987 3 года назад

    Thanks a lot ... you really did cleared my doubt which I had since long and which made me feel partial Fractions are tough due to that doubt...
    Thanks again....

  • @ghinee9105
    @ghinee9105 3 года назад

    U make it look easier using this method

  • @rohansharma3718
    @rohansharma3718 3 года назад +1

    thank you❤️❤️❤️

  • @snotgobbeler
    @snotgobbeler 9 лет назад +2

    hi, find your videos really useful, but i just dont seem to be able to grasp how when initially expanding out the brackets into A B and C, the C denominator is (x+3)^2, surely this is could further be factored out into its (X+3)(X+3) components and then we would have too many (X+3)'s i noticed that you mentioned in the previous video (example4) that you said if it was X^20 that there would be A/X^1 + B/X^2 + c/X^3.... all the way upto T/X^20. I simply cannot understand this because if they were all multiplied together they wouldnt equal X^20, they would equal X^20factoral. Thanks for the great videos but im struggling to understand this little part. could you please expand on it a little bit.
    Thanks

    • @rdyjur
      @rdyjur 8 лет назад +2

      Yeah I wish someone could explain this. I'm simply doing the steps beause it's what I've been told, with no understanding of why.... :/

  • @wikyo77
    @wikyo77 13 лет назад +1

    How can you remember all this!? By the way, you're the best. Thank you.

  • @jeevanmangalagiri1386
    @jeevanmangalagiri1386 3 года назад

    Incredible mann!!!

  • @asmaiqbal9610
    @asmaiqbal9610 5 лет назад

    Superbly explained

  • @darvinraj4339
    @darvinraj4339 10 лет назад

    helped me so much ... thank u so much

  • @HuntedGamerFilms
    @HuntedGamerFilms 11 лет назад

    Great video I only had 2 days to learn this in class and we are having a quiz and test in the next 2 days.

  • @terrellwebb2899
    @terrellwebb2899 7 лет назад +1

    If you were to teat the first equation (x+1)+(x+3)+(x+3) as a case 1 (linear) would i get the same answer, or is it totally wrong to do that?

  • @thusithalexander5196
    @thusithalexander5196 11 лет назад

    Man..u r good @ this..keep it up..

  • @yongxinlim6156
    @yongxinlim6156 3 года назад

    thanks, this help me a lot.
    thank you very much.

  • @edwardrk35
    @edwardrk35 6 месяцев назад

    so useful bro thankyou

  • @elvisili
    @elvisili 6 лет назад

    Fantastic tutorial, thanks

  • @KnowledgeIgnite
    @KnowledgeIgnite 11 лет назад +6

    clear explaination..........thanksssss

  • @cyclotron1295
    @cyclotron1295 5 лет назад

    Thanks for this .I was confused in taking LCM

  • @xaviercalapuja792
    @xaviercalapuja792 3 года назад

    Excelente explicación , me ayudaste un montón

  • @aashishchy1
    @aashishchy1 Год назад

    Thank you so much ❤

  • @sabelozwane6917
    @sabelozwane6917 9 лет назад

    Awesome.. great explanation...thank you very much

  • @tavleensingh1363
    @tavleensingh1363 6 лет назад

    Thnx now i can solve partial fraction sums

  • @freshkidotv8550
    @freshkidotv8550 Год назад

    Better understanding. Thanks

  • @patrickjmt
    @patrickjmt  14 лет назад

    @blkteg21 thanks very much : )

  • @edwardnese
    @edwardnese 13 лет назад +2

    why would there be an x+3 and x+3^2 instead of just two x+3

    • @yaiu8353
      @yaiu8353 4 года назад +1

      This has yet to be answered

  • @williamfry4289
    @williamfry4289 11 лет назад

    do you need to add +C to the end?

  • @candiceford88
    @candiceford88 3 года назад

    Thanks, didn't learn this

  • @ridhima1933
    @ridhima1933 7 месяцев назад

    Thanks sir. So good

  • @JKhal
    @JKhal 5 лет назад

    i honestly used the one method he mentioned about subbing values for "x" to cancel certain A,B,C coefficients, it took me 2 min to do the problem

  • @vaibhavrokde4405
    @vaibhavrokde4405 5 лет назад

    Helped a lot

  • @adil4ch
    @adil4ch 11 лет назад

    what do you do after the end to integrate it?

  • @dSlashMetal
    @dSlashMetal 11 лет назад +6

    Thanks a lot good sir. I mean you said you could also shortcut to solve for A and C, then plug it in the system for B. Would be quicker, thank you for the explanation!

  • @axpence
    @axpence 12 лет назад

    After you find A B and C you simply integrate each fraction separately . Normally you get something like A*ln|some function | +/- B*ln|some function| ... etc.

  • @amruthasankar3453
    @amruthasankar3453 2 года назад +1

    Thankyouuuuu so muchhhhh sirrrr❤️❤️❤️❤️❤️❤️❤️❤️❤️🤗🤗🤗🤗🤗🥰🥰🥰🥰your classess are such an amazing and easily understood for everyone🤗🤗🤗🥰🥰🥰🥰🥰🥰❤️❤️❤️❤️the way of explain is so beautiful❤️❤️❤️❤️❤️🤗🤗🤗🤗God bless you more and more🙌🙌🙌🙌🙌🌸🌸🌸🌸🌸🌸🌸🌸🌸🌸

  • @haniadar2929
    @haniadar2929 6 лет назад

    Thank you so much You save me :)

  • @Juxtaroberto
    @Juxtaroberto 11 лет назад

    Personally, I noticed that if you foil out the denominator, you get a difference of squares, so I might try factoring out a -10, to reverse the order in the denominator and get rid of the constant, and now I'd have an integral that looks like it'd end up being the inverse tangent hyperbolic function...

  • @nehasathe7827
    @nehasathe7827 5 лет назад

    I have a question...why don't we do long division in this problem? Isn't the numerator supposed to be a degree less than the denominator?

  • @IngaMitinyan
    @IngaMitinyan 9 лет назад +1

    Thanks soo much! I have a question, it might be very silly. How is it that we are allowed to multiply by (-1)? Doesn't this operation mess up the values?

    • @108mtsan
      @108mtsan 9 лет назад

      No, it doesn't mess up the values because you're multiplying both sides of the equation by -1. By multiplying both sides, the values remain the same ratio or equivalent as before.
      +Inga M

    • @IngaMitinyan
      @IngaMitinyan 9 лет назад

      +Michael Tsang I appreciate your answer!

    • @ndurhkhumalolo-keyz2620
      @ndurhkhumalolo-keyz2620 2 года назад

      Do we always multiple by (-1) ??

  • @aclwitt
    @aclwitt 12 лет назад

    In example 6 you use Bx + C over the polynomial of degree 2, here (x+3)^2 only gets a C, why is that exactly? Thanks!

  • @sonyareynolds8753
    @sonyareynolds8753 7 лет назад

    When you equate the coefficients, can you use a matrix to solve the system patrickjmt?

    • @intothevortex7825
      @intothevortex7825 7 лет назад

      Sonya Reynolds yes u can. Its much faster. The form is AX=B and u solve by premultiply A^-1 to both sides as (A^-1)A = 1 therefore X=(A^-1)B. This is matrix solution. Easier when you dealing with 4+ variables