Answer
$=2,\qquad x\neq-2,2$
Work Step by Step
Factor what you can:
$x^{2}-4=$ difference of squares $= (x-2)(x+2)$
$x^{2}-4x+4$= square of a difference = $(x-2)^{2}$
$2x-4=2(x-2)$
$x+2$ is factored
Expression $=\displaystyle \frac{(x+2)(x-2)}{(x-2)^{2}}\cdot\frac{2(x-2)}{x+2}$
$\qquad$
...exclude the values that yield 0 in the denominator:
$x\neq-2,2$
... cancel common factors: $(x-2),\ (x-2)$ and $(x+2)$
$=\displaystyle \frac{2}{1},\qquad x\neq-2,2$
$=2,\qquad x\neq-2,2$
