#### Answer

$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}=\dfrac{a+3}{a+2}$

#### Work Step by Step

$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}$
Factor the numerator and the denominator of the first fraction:
$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}=\dfrac{(a-2)^{2}}{(a-2)(a+2)}\cdot\dfrac{a+3}{a-2}=...$
Multiply the two rational expressions and simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{(a-2)^{2}(a+3)}{(a-2)^{2}(a+2)}=\dfrac{a+3}{a+2}$