Determining Coefficients for Partial Fractions

( • ❖ Partial Fraction Dec... )
( • Determining Coefficien... )
( • ❖ Harder Partial Fract... )
( • A Complete Partial Fra... )
( • Integration Using meth... )
( • Partial Fraction Decom... )
( • A Complete Partial Fra... ) Determining Coefficients for Partial Fractions: All Four Cases Explained!
In this video, I’ll show you how to determine coefficients for partial fractions by covering all four cases:
Distinct linear factors
Distinct linear factors, some repeated
Distinct quadratic factors
Distinct quadratic factors, some repeated
You’ll learn how to break down complex rational functions into simpler fractions, making integration easier. We’ll go through examples that involve different combinations of linear and quadratic factors, explaining the reasoning behind each step. These concepts are crucial when solving integrals involving partial fractions.
What You Will Learn:
How to decompose rational functions using partial fractions.
How to handle distinct and repeated linear factors.
How to manage distinct and repeated quadratic factors.
Step-by-step examples for determining coefficients in all cases.
Techniques to integrate using partial fractions.
By the end of this video, you’ll have a solid understanding of how to determine coefficients in all types of partial fractions, preparing you for more advanced calculus problems.
Don’t forget to comment if you find the video helpful, like, share, and subscribe to the channel! Tell your friends, teachers, or parents about these lessons if you think they’ll benefit from them.
Support me on Patreon if you'd like to see more content: www.patreon.co...
#IntegrationByPartialFractions #MathTutorials #RationalFunctions #AdvancedCalculus #MathPractice #StudyMath #LearnCalculus #Mathematics #AlgebraHelp

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yes, it is a mistake that tons have pointed out in the comments as well as the annotations

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I don't think I was the only one who noticed, but I guess you got it wrong on the last part... It should be 3 instead of 0. I hope you don't do the same mistake again, but so far so good... you really are a good teacher and you did great tho. I really learned a lot on making up the tedious parts especially on doing manipulations. thank you patrick :)

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I knew the cases but didn't know when exactly to apply them, especially the repeated factors....thanks for showing me how to approach it. Great explaination. I have a test on partial fractions, graphing rational functions and quadratic roots. YOU GIVE ME HOPE!!!

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@ClownDatWalk for the first year and first few hundred videos, it was simply just something to do; then google started its partner program so i do now get a cut of the ad revenue that google makes from my vids. it was never my intent to make money from the videos, just a nice opportunity that came up along the way. thanks to their program, i am able to cut back on my tutoring job which is why i have been able to post many more videos this past year

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The constant, shouldnt it be B+4c+4d=3 ??

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You got confused from all the zeros, so you put the constant terms, B+4C+4D, equal to zero aswell when it really should be equal to 3. Great job with the explaning though, really helped me alot!:)

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hey, i believe you missed the coefficient of the constant value on the last problem. it should be B + 4C + 4D = 3 not equal to zero as you put. You may have just overlooked it as it was a long problem. Thanks btw for all these videos, i've been using them for the past three years (from high school to college) for review. They're extremely helpful

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A= -6/25, B= -9/25, C=6/25, D=3/5 are these values correct?

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Garrett Munson I got those exact same values

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Why didn't you include =3 in the 4th equation? I think that is also what made me get different answers if I used the other equations.

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