how do I get the answer shown in the attached problem? when I tried it out, I couldn't get the numerator to 1.

Thanks!

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- Jun 2nd 2010, 08:41 AMcalculus0partial fractions
how do I get the answer shown in the attached problem? when I tried it out, I couldn't get the numerator to 1.

Thanks! - Jun 2nd 2010, 09:10 AMUnknown008
First, factor your denominator.

remember that:

$\displaystyle a^2 - b^2 = (a+b)(a-b)$

Can you do it now? - Jun 2nd 2010, 07:31 PMmr fantastic
- Jun 7th 2010, 07:28 PMwilly0625
We write

$\displaystyle \frac{2}{1-x^2}=\frac{2}{(1-x)(1+x)}=\frac{A}{1-x}+\frac{B}{1+x}_{.}$

With a bit of algebraic manipulation of the above equality(actually identity), we can find out that

$\displaystyle A = B = 1$.(There are several ways to do this. One of them is writing the right hand side as a single fraction and we get an equation by equating the denominator with 2)

So we have

$\displaystyle -1+\frac{2}{1-x^2} = -1 + \frac{2}{(1-x)(1+x)} = 1 +\frac{1}{1-x}+\frac{1}{1+x}_{.}$