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Math Help - Partial Fractions Question

  1. #1
    Super Member
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    Partial Fractions Question

    Hi
    Need help on the following questions:
    1) Resolve into partial fractions: \frac{x^2-x+1}{(4x^2-1)(x-2)}

    This is what i have done:
    \frac{x^2-x+1}{(4x^2-1)(x-2)} => \frac{x^2-x+1}{(x-2)(2x-1)(2x+1)}

    \frac{A}{(x-2)}+\frac{B}{(2x-1)}+\frac{C}{(2x+1)}

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

    A(4x^2-1)+B(2x^2-3x-2)+C(2x^2-5x+2)=x^2-x+1

    Let x = 2

    15A=1

    A=\frac{1}{15}

    Let x = \frac{1}{2}

    \frac{-6}{2}B=1

    B=\frac{-2}{6}

    Let x= \frac{-1}{2}

    \frac{10}{2}C=1

    C=\frac{1}{5}

    \frac{\frac{1}{15}}{(x-2)}+\frac{\frac{-2}{6}}{(2x-1)}+\frac{\frac{1}{5}}{(2x+1)}

    book's answer says it \frac{\frac{1}{5}}{(x-2)}-\frac{\frac{1}{4}}{(2x-1)}+\frac{\frac{7}{20}}{(2x+1)}

    someone tell me where i have gone wrong.

    P.S
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  2. #2
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    let A=2
    then 15=3A not 15=A
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  3. #3
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    Zhangyi05 means "Let x= 2".
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  4. #4
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    thanks i understand now.
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