Answer
$\dfrac{b+2a}{2b+a}$
Work Step by Step
The given expression, $
\dfrac{(2a)^{-1}+b^{-1}}{a^{-1}+(2b)^{-1}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{1}{2a}+\dfrac{1}{b^1}}{\dfrac{1}{a^1}+\dfrac{1}{(2b)^1}}
\\\\=
\dfrac{\dfrac{b+2a}{2ab}}{\dfrac{2b+a}{2ab}}
\\\\=
\dfrac{\dfrac{b+2a}{\cancel{2ab}}}{\dfrac{2b+a}{\cancel{2ab}}}
\\\\=
\dfrac{b+2a}{2b+a}
.\end{array}
