Originally Posted by

**kkm** Given the following problem:

$\displaystyle \left(\frac{x^2-2x+1}{x^2+x}.\frac{2x+1}{x^2-x}\right)^{-1}+\frac{x^3-x}{(x+1)^2-x^2}$

Is my answer correct?

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

$\displaystyle = \left(x-1\right)^{-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}$

$\displaystyle = \frac{1}{x-1}+\frac{x(x+1)(x-1)}{(x+1-x)(x+1+x)}$

$\displaystyle = \frac{1(x+1-x)(x+1+x)+x(x+1)(x-1)}{(x-1)(x+1-x)(x+1+x)}$

Answer:

$\displaystyle (x+1)^2$

I am not sure if that is correct, and would love someone to review my process, as I tried to be as detailed as possible.