Answer
$\dfrac{22z-45}{3z(z-3)}$
Work Step by Step
Factoring the given expression, $
\dfrac{7}{3z-9}+\dfrac{5}{z}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{7}{3(z-3)}+\dfrac{5}{z}
.\end{array}
Using the $LCD=
3z(z-3)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{z(7)+3(z-3)(5)}{3z(z-3)}
\\\\=
\dfrac{7z+15z-45}{3z(z-3)}
\\\\=
\dfrac{22z-45}{3z(z-3)}
.\end{array}
