Answer
$\frac{a+b}{a^2-ab+b^2}$
Work Step by Step
Step 1. Factor the denominators: $a^3+b^3=(a+b)(a^2-ab+b^2)$ and $a^2+2ab+b^2=(a+b)^2$
Step 2. Use the above results in the original expression, we have:
$\frac{\frac{1}{a^3+b^3}}{\frac{1}{a^2+2ab+b^2}}=\frac{\frac{1}{(a+b)(a^2-ab+b^2)}}{\frac{1}{(a+b)^2}}=\frac{(a+b)^2}{(a+b)(a^2-ab+b^2)}=\frac{a+b}{a^2-ab+b^2}$
