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Math Help - Partial Fraction Decomposition

  1. #1
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    Partial Fraction Decomposition

    All I need to do is write the form of the partial function (I don't have to find the numerical values) of this:

    x2/(x2-2x-2) partial fraction decomposition

    I know the rule of quadratic factor is Ax+B/ax2+bx+c

    so wouldn't it be Ax+B/x2+2x+2 or am I missing something? Kind of confused...
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  2. #2
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    Re: Partial Fraction Decomposition

    Hello, Steelers72!

    I don't understand the question.
    The problem can be solved without Partial Fractions.


    All I need to do is write the form of the partial function.
    I don't have to find the numerical values.

    . . . \frac{x^2}{x^2 -2x-2}

    First of all, the fraction is "improper" . . . Use long division.

    . . \frac{x^2}{x^2-2x-2} \;=\;1 + \frac{2x + 2}{x^2-2x-2}


    Second, are we suppose to factor that quadratic?
    . . . . x^2 - 2x - 2 \;=\;\big[x - (1+\sqrt{3})\big]\,\bog[x - (1-\sqrt{3})\big]

    . . Then work on: . \frac{2x+2}{x^2-2x-2} \;=\;\frac{A}{x-1-\sqrt{3}} + \frac{B}{x - 1 + \sqrt{3}} .(ugh!)


    Or should we solve: . \frac{2x+2}{x^2-2x-2} \;=\;\frac{Ax}{x^2-2x-2} + \frac{B}{x^2-2x-2}

    Would it surprise you to learn that A = 2 and B = 2\,?
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  3. #3
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    Re: Partial Fraction Decomposition

    Wow! Thank you for that brilliant walk-through! Sorry for the question wording; it was asking just to find out the form of the partial fraction decomposition of the function

    ie. Given 5x/x^2 +x -6

    = A/x+3 B/x-2

    That's all they wanted
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