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Math Help - partial fraction query

  1. #1
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    partial fraction query

    hi - I've got an intergral to solve but when seperating this fraction get a different answer to my Maple solution. Take a look and show me where i'm going wrong because i'm stumped!

    \frac{x+2}{1-4x^2}
    i) =\frac{x+2}{(1-2x)(1+2x)}
    ii) =\frac{5}{4(1-2x)} + \frac{3}{4(1+2x)}

    but my program tells me its =\frac{-5}{4(1-2x)} + \frac{3}{4(1+2x)}

    I can't see why the negative sign is introduced. Any ideas??

    Cheers, F
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  2. #2
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    Re: partial fraction query

    Hello, FelixHelix!

    Your work is absolutely correct.

    Maple is wrong . . . I have no idea why.

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  3. #3
    Super Member Quacky's Avatar
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    Re: partial fraction query

    Edit: Beaten to it.

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

    \rightarrow A(1+2x)+B(1-2x)=x+2

    Let x=\frac{1}{2}

    2A=\frac{5}{2}

    A=\frac{5}{4}

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

    2B=\frac{3}{2}

    B=\frac{3}{4}

    As far as I can tell there isn't an error with your work. Wolfram Alpha agrees in this respect, but not this one, so I wonder whether there's some sort of problem with their Gaussian Elimination or something.
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  4. #4
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    Re: partial fraction query

    Quote Originally Posted by FelixHelix View Post
    hi - I've got an intergral to solve but when seperating this fraction get a different answer to my Maple solution. Take a look and show me where i'm going wrong because i'm stumped!
    I wonder if you are reading Maple correctly?
    The program gives me \frac{-5}{4(2x-1)}+\frac{3}{4(2x+1)}.

    But that is the same as \frac{5}{4(1-2x)}+\frac{3}{4(1+2x)}
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  5. #5
    Super Member Quacky's Avatar
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    Re: partial fraction query

    Reading the given answer carefully is something I'll have to pay more attention to.
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  6. #6
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    Re: partial fraction query

    Quote Originally Posted by Plato View Post
    I wonder if you are reading Maple correctly?
    The program gives me \frac{-5}{4(2x-1)}+\frac{3}{4(2x+1)}.

    But that is the same as \frac{5}{4(1-2x)}+\frac{3}{4(1+2x)}

    You're absolutely right Plato! Thanks for this - I'll take care in reading off in the future...

    All the best
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