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Thread: partial fractions

  1. #1
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    partial fractions

    Hi I am trying to solve the following problem: find the constant A0, A1, A2 such that

    $\displaystyle \frac{1}{(1+(a0)x^2-i(b0)x)(1+(a1)x^2-i(b1)x)(1+(a2)x^2-i(b2)x)}$
    =$\displaystyle \frac{A0}{(1+(a0)x^2-i(b0)x)}$+$\displaystyle \frac{A1}{(1+(a1)x^2-i(b1)x)}$+$\displaystyle \frac{A2}{(1+(a2)x^2-i(b2)x)}$

    That s drives me mad! Any help for me please.[/quote]
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  2. #2
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    Multiply $\displaystyle
    \frac{A0}{(1+(a0)x^2-i(b0)x)}$+$\displaystyle \frac{A1}{(1+(a1)x^2-i(b1)x)}$+$\displaystyle \frac{A2}{(1+(a2)x^2-i(b2)x)}$

    by $\displaystyle ({(1+(a0)x^2-i(b0)x)(1+(a1)x^2-i(b1)x)(1+(a2)x^2-i(b2)x)})$

    you should be left with this, and solve.

    $\displaystyle (A0)(1+(a1)x^2-i(b1)x)(1+(a2)x^2-i(b2)x)$$\displaystyle +(A1)(1+(a0)x^2-i(b0)x)(1+(a2)x^2-i(b2)x)$
    $\displaystyle +(A2)(1+(a0)x^2-i(b0)x)(1+(a1)x^2-i(b1)x)$
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  3. #3
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    Hi thank you for your help. However, solving this
    =1 then?? but only one equation for 3 unknown constants? How is possible ?
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