Answer
$\dfrac{5z+6}{(z+3)(z-3)}$
Work Step by Step
Factoring the given expression, $
\dfrac{3z}{z^2-9}-\dfrac{2}{3-z}
,$ results to
\begin{array}{l}
\dfrac{3z}{(z+3)(z-3)}-\dfrac{2}{-(z-3)}
\\\\=
\dfrac{3z}{(z+3)(z-3)}+\dfrac{2}{z-3}
.\end{array}
Using the $LCD=
(z+3)(z-3)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{1(3z)+(z+3)(2)}{(z+3)(z-3)}
\\\\=
\dfrac{3z+2z+6}{(z+3)(z-3)}
\\\\=
\dfrac{5z+6}{(z+3)(z-3)}
.\end{array}
