Answer
$\dfrac{34-9a}{15(a-2)}$
Work Step by Step
The expression $
\dfrac{5}{3a-6}-\dfrac{a}{a-2}+\dfrac{3+2a}{5a-10}
$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{5}{3(a-2)}-\dfrac{a}{a-2}+\dfrac{3+2a}{5(a-2)}
\\\\=
\dfrac{5(5)-15a+3(3+2a)}{15(a-2)}
\\\\=
\dfrac{25-15a+9+6a}{15(a-2)}
\\\\=
\dfrac{34-9a}{15(a-2)}
.\end{array}
