In order to simplify this expression, we can do the following steps:
[tex]\begin{gathered} \frac{(x-2)^2}{x+2}\colon\frac{x-2}{x^2-4} \\ =\frac{(x-2)^2}{x+2}\cdot\frac{x^2-4}{x-2_{}} \\ =\frac{(x-2)^2}{x+2}\cdot\frac{\mleft(x+2\mright)\mleft(x-2\mright)}{x-2} \\ =\frac{(x-2)^2}{x+2}\cdot x+2 \\ =(x-2)^2 \end{gathered}[/tex]So the correct option is C.
