#### Answer

$\frac{b+2a}{2b+a}$

#### Work Step by Step

$\frac{(2a)^{-1}+(b)^{-1}}{(a)^{-1}+(2b)^{-1}}$
=$\frac{\frac{1}{2a}+\frac{1}{b}}{\frac{1}{a}+\frac{1}{2b}}$
=$\frac{\frac{b+2a}{2ab}}{\frac{2b+a}{2ab}}$
=$\frac{b+2a}{2ab}\div\frac{2b+a}{2ab}$
=$\frac{b+2a}{2ab}\times \frac{2ab}{2b+a}$
=$\frac{b+2a}{2b+a}$