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Math Help - Error on paper

  1. #1
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    Error on paper

    A student of mine has handed me a test paper that was given to him at school. It seems to me there is a mistake on it, but I want to make absolutely sure. Here is the question:

    Express \frac{x^{2}-6x+1}{(x^2+1)(x^2-1)} in Partial Fractions

    Hence show that \frac{\mathrm{d} }{\mathrm{d} x}\left \{\frac{x^{2}-6x+1}{(x^2+1)(x^2-1)}  \right \} when x=2 is \frac{28}{45}

    I get \frac{194}{225}
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Error on paper

    Thanks from grillage
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    Re: Error on paper

    Hey grillage.

    For this kind of thing I use a computer package to eliminate the human error aspect. Using Wolfram Alpha, we get:

    d/dx((x^2 - 6x + 1)/((x^2+1)*(x^2-1))) - Wolfram|Alpha

    Plugging in x = 2 gives us

    dy/dx|x = 2 = 194/225 which is in agreement with your value.
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    Re: Error on paper

    How does the partial fraction expansion help you to get the derivative?

    - Hollywood
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