$\begin{array}{l}\text { 1. }\left(\frac{a^{2}+2 b^{2}}{a+b}-\frac{b^{3}-a^{2} b}{a^{2}+2 a b+b^{2}}\right)+ \\ \frac{a^{3}-b^{3}}{a^{2}-a b-2 b^{2}} ;\end{array}$
$\begin{array}{l}\text {-1. Solution: Original expression }=\left[\frac{a^{2}+2 b^{2}}{a+b}+\right. \\ \left.\frac{b(a+b)(a-b)}{(a+b)^{2}}\right] \div \frac{a^{3}-b^{3}}{a^{2}-a b-2 b^{2}} \\ =\frac{a^{2}+a b+b^{2}}{a+b} \cdot \frac{(a-2 b)(a+b)}{(a-b)\left(a^{2}+a b+b^{2}\right)} \\ =\frac{a-2 b}{a-b} .\end{array}$