Answer
$\dfrac{9a+6}{4a-8}$
Work Step by Step
The expression $
\dfrac{\dfrac{3}{2+a}+\dfrac{6}{2-a}}{\dfrac{5}{a+2}-\dfrac{1}{a-2}}
$ simplifies to
\begin{array}{l}
\dfrac{\dfrac{3}{a+2}-\dfrac{6}{a-2}}{\dfrac{5}{a+2}-\dfrac{1}{a-2}}
\\\\=
\dfrac{\dfrac{3(a-2)+6(a+2)}{(a+2)(a-2)}}{\dfrac{5(a-2)-1(a+2)}{a+2}}
\\\\=
\dfrac{3(a-2)+6(a+2)}{5(a-2)-1(a+2)}
\\\\=
\dfrac{3a-6+6a+12}{5a-10-a-2}
\\\\=
\dfrac{9a+6}{4a-8}
.\end{array}
