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Math Help - Confirmation needed .

  1. #1
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    Confirmation needed .

    Expand \frac{5x}{(1-2x)(2+x)} in ascending powers of x up to and including the term in x^3

    I tried :

    After partial fracting , i got \frac{1}{1-2x}-\frac{2}{2+x}

    =(1-2x)^{-1}-4(1+\frac{x}{2})^{-1}

    =1+2x+4x^2+8x^3-4+2x-x^2+\frac{1}{2}x^3

    =-3+4x+3x^2+\frac{17}{2}x^3

    which is wrong according to the book .
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  2. #2
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    Power series

    Hello thereddevils
    Quote Originally Posted by thereddevils View Post
    Expand \frac{5x}{(1-2x)(2+x)} in ascending powers of x up to and including the term in x^3

    I tried :

    After partial fracting , i got \frac{1}{1-2x}-\frac{2}{2+x}

    =(1-2x)^{-1}-\color{red}4\color{black}(1+\frac{x}{2})^{-1}

    =1+2x+4x^2+8x^3-4+2x-x^2+\frac{1}{2}x^3

    =-3+4x+3x^2+\frac{17}{2}x^3

    which is wrong according to the book .
    \frac{2}{2+x}= \color{red}1\color{black}(1+\frac{x}{2})^{-1}

    Grandad
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  3. #3
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    oh thanks ... so is my working before the mistake correct ?
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  4. #4
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    Power series

    Hello thereddevils
    Quote Originally Posted by thereddevils View Post
    oh thanks ... so is my working before the mistake correct ?
    Yes.

    I make the final answer

    \frac{5x}{2}+\frac{15x^2}{4}+\frac{65x^3}{8}

    Does that agree with your book?

    Grandad
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  5. #5
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    Absolutely yes , thanks for helping out .
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