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Math Help - Partial Fractions

  1. #1
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    Partial Fractions

    Write out the form of the partial fraction deconposition of the function. Do not determine the numerical values of the coefficients.
    b. (x^2)/(x^2+x+2)

    what i got was 1 - (x+2)/(x^2+x+2) and i don't have any A or B things in it so I dont know what i did wrong.. should it be 1- (Ax+B)/(x^2+x+2)??
    is there a general formula that I missed?
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  2. #2
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    you can't use partial fractions, because the denominator is irreducible on \mathbb R.
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  3. #3
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    Quote Originally Posted by Jasonium View Post
    Write out the form of the partial fraction deconposition of the function. Do not determine the numerical values of the coefficients.
    b. (x^2)/(x^2+x+2)

    what i got was 1 - (x+2)/(x^2+x+2) and i don't have any A or B things in it so I dont know what i did wrong.. should it be 1- (Ax+B)/(x^2+x+2)??
    is there a general formula that I missed?
    What you've done is as far as it can go.
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  4. #4
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    \frac{x^2}{x^2+x+2} = 1 - \frac{x-2}{x^2 + x + 2}

    We cannot factorize x^2+x+2 over \mathbb{R}, but we can over \mathbb{C}. So for some A,B \in \mathbb{C},

    \frac{x-2}{x^2 + x + 2} \equiv \frac{A}{x-\alpha} + \frac{B}{x-\beta}

    Where \alpha = \frac{-1-i\sqrt{7}}{2}, \beta = \frac{-1+i\sqrt{7}}{2}
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