Answer
$\dfrac{5}{6}$
Work Step by Step
The given expression, $
\dfrac{2a^{-1}+(2a)^{-1}}{a^{-1}+2a^{-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{2}{a}+\dfrac{1}{2a}}{\dfrac{1}{a}+\dfrac{2}{a}}
\\\\=
\dfrac{\dfrac{4+1}{2a}}{\dfrac{1+2}{a}}
\\\\=
\dfrac{\dfrac{5}{2a}}{\dfrac{3}{a}}
\\\\=
\dfrac{5}{2a}\div\dfrac{3}{a}
\\\\=
\dfrac{5}{2a}\cdot\dfrac{a}{3}
\\\\=
\dfrac{5}{2\cancel{a}}\cdot\dfrac{\cancel{a}}{3}
\\\\=
\dfrac{5}{6}
.\end{array}
