express in simplest form:
I get to here $\displaystyle (x(x-2))/(x(x+2))+(-4)/(x+2)$
now what do I do?
the key here is a little factoring, and the rewriting of some of the terms
$\displaystyle x^2-4=(x+2)(x-2)$
$\displaystyle x^2-4x+4=(x-2)^2$
and finally dividing by $\displaystyle \frac{4}{x^2-4x+4}$ is the same as multiplying by
$\displaystyle \frac{(x-2)^2}{4}$
So rewrting we have
$\displaystyle \frac{2x}{(x-2)(x+2)}\cdot\frac{(x-2)^2}{4}+\frac{1}{(x-2)(x+2)}\cdot\frac{-(x-2)}{3}$
can you go from there?