Answer
$\dfrac{-a^2+31a+10}{5(a-6)(a+1)}$
Work Step by Step
The factored form of the given expression, $
\dfrac{2}{a-6}+\dfrac{3a}{a^2-5a-6}-\dfrac{a}{5a+5}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2}{a-6}+\dfrac{3a}{(a-6)(a+1)}-\dfrac{a}{5(a+1)}
.\end{array}
Using the $LCD=
5(a-6)(a+1)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{5(a+1)(2)+5(3a)-(a-6)(a)}{5(a-6)(a+1)}
\\\\=
\dfrac{10a+10+15a-a^2+6a}{5(a-6)(a+1)}
\\\\=
\dfrac{-a^2+(10a+15a+6a)+10}{5(a-6)(a+1)}
\\\\=
\dfrac{-a^2+31a+10}{5(a-6)(a+1)}
.\end{array}
