## Algebra: A Combined Approach (4th Edition)

$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}=\dfrac{a+3}{a+2}$
$\dfrac{a^{2}-4a+4}{a^{2}-4}\cdot\dfrac{a+3}{a-2}$ 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: $...=\dfrac{(a-2)^{2}(a+3)}{(a-2)^{2}(a+2)}=\dfrac{a+3}{a+2}$