Answer
$\dfrac{5+2x}{x(x-3)}$
Work Step by Step
Factoring the given expression, $
\dfrac{5}{x^2-3x}+\dfrac{4}{2x-6}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{5}{x(x-3)}+\dfrac{4}{2(x-3)}
.\end{array}
Using the $LCD=
2x(x-3)
$, the expression above simplifies to
\begin{array}{l}
\dfrac{2(5)+x(4)}{2x(x-3)}
\\\\=
\dfrac{10+4x}{2x(x-3)}
\\\\=
\dfrac{2(5+2x)}{2x(x-3)}
\\\\=
\dfrac{\cancel{2}(5+2x)}{\cancel{2}x(x-3)}
\\\\=
\dfrac{5+2x}{x(x-3)}
.\end{array}