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express x-1/(x+1)(x-2)^2 into partial fractions

  • maths -

    let
    (x-1)/((x+1)(x-2)^2) = A/(x-1) + B/(x-2) + C/(x-2)^2

    multiply both sides by (x+1)(x-2)^2

    A(x-2)^2 + B(x-2)(x+1) + C(x+1) = x-1

    let x = 2, ---> 3C = 1 or C=13
    let x = -1 ---> 9A + -2 or A = -2/9
    let x = 0 ----> 4A - 2B + C = -1
    4(-2/9) - 2B + 1/3 = -1
    times 9
    -8 - 18B + 3 = -9
    B = 2/9

    so (x-1)/(x-2)^2 = -2/(9(x+1)) + 2/(9(x-2)) + 1/(3(x-2)^2)

    verified with Wolfram:
    http://www.wolframalpha.com/input/?i=%28x-1%29%2F%28%28x%2B1%29%28x-2%29%5E2%29

  • typo - maths -

    in the middle of the solution above the line should read:

    et x = 2, ---> 3C = 1 or C=1/3

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