# Thread: partial fractions

1. ## 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]

2. 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)$
$\displaystyle +(A2)(1+(a0)x^2-i(b0)x)(1+(a1)x^2-i(b1)x)$

3. Hi thank you for your help. However, solving this
=1 then?? but only one equation for 3 unknown constants? How is possible ?