Answer
$\dfrac{3m^2+2m-12}{5(m+2)}$
Work Step by Step
The given expression, $
\dfrac{3+\dfrac{2m}{m^2-4}}{\dfrac{5}{m-2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\dfrac{3(m^2-4)+2m}{m^2-4}}{\dfrac{5}{m-2}}
\\\\=
\dfrac{\dfrac{3m^2-12+2m}{m^2-4}}{\dfrac{5}{m-2}}
\\\\=
\dfrac{3m^2+2m-12}{m^2-4}\div\dfrac{5}{m-2}
\\\\=
\dfrac{3m^2+2m-12}{(m+2)(m-2)}\cdot\dfrac{m-2}{5}
\\\\=
\dfrac{3m^2+2m-12}{(m+2)(\cancel{m-2})}\cdot\dfrac{\cancel{m-2}}{5}
\\\\=
\dfrac{3m^2+2m-12}{5(m+2)}
.\end{array}
