QuestionDivide as indicated. Simplify the answer. $$\begin{array}{l} \frac{a-b}{4 a+4 b} \div \frac{a^{2}-b^{2}}{a^{2}+6 a+9} \\ \frac{a-b}{4 a+4 b} \div \frac{a^{2}-b^{2}}{a^{2}+6 a+9}=\square \end{array}$$ $\square$

Studdy Solution
Substitute the factored forms into the expression:
$\frac{a-b}{4(a+b)} \times \frac{(a+3)^2}{(a-b)(a+b)}$
Cancel common factors:
1. Cancel $a-b$ in the numerator and denominator.
2. Cancel $a+b$ in the numerator and denominator.
The simplified expression is:
$\frac{(a+3)^2}{4}$
The simplified answer is:
$\boxed{\frac{(a+3)^2}{4}}$