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Math Help - Partial fraction decomposition

  1. #1
    Member OnMyWayToBeAMathProffesor's Avatar
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    Question Partial fraction decomposition

    hello,

    i have a problem i am stuck on. i have figured it out till the very end but can not find the answer.here it is.

    The Problem : Find the partial fraction decomposition.
    (-x+10)/(x^2+x-12)

    here is what i got from that problem.

    (-x+10)/(x+4)(x-3) = (A/(x+4))+(B/(x-3))

    (-x+10)=A(x-3)+B(x+4)

    (-x+10)=Ax-3A+Bx+B4

    -1=A+B

    10= (-3a)+(b4)

    What is A and B so (A/(x+4))+(B/(x-3)) = (-x+10)/(x+4)(x-3)

    Thank you.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by OnMyWayToBeAMathProffesor View Post
    hello,

    i have a problem i am stuck on. i have figured it out till the very end but can not find the answer.here it is.

    The Problem : Find the partial fraction decomposition.
    (-x+10)/(x^2+x-12)

    here is what i got from that problem.

    (-x+10)/(x+4)(x-3) = (A/(x+4))+(B/(x-3))

    (-x+10)=A(x-3)+B(x+4)

    (-x+10)=Ax-3A+Bx+B4

    -1=A+B

    10= (-3a)+(b4)

    What is A and B so (A/(x+4))+(B/(x-3)) = (-x+10)/(x+4)(x-3)

    Thank you.
    (write 4B instead of B4)

    so i guess you are having trouble solving the simultaneous equations?

    here's another approach

    -x + 10 = A(x - 3) + B(x + 4)

    Let x = 3 \implies -3 + 10 = 7B
    Let x = -4 \implies 4 + 10 = -7A

    there you have your A and B


    the method you were attempting was the equating coefficients method, i don't see the problem you have, the only thing left for you to do is to solve the simultaneous equations
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  3. #3
    Member OnMyWayToBeAMathProffesor's Avatar
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    Reply

    thank you, i figured out how to do it in matrix form.
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