Answer
$\dfrac{5+2x}{x(x-7)}$
Work Step by Step
Factoring the given expression, $
\dfrac{5}{x^2-7x}+\dfrac{4}{2x-14}
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{5}{x(x-7)}+\dfrac{4}{2(x-7)}
.\end{array}
Using the $LCD=
2x(x-7)
$, the expression above simplifies to
\begin{array}{l}\require{cancel}
\dfrac{2(5)+x(4)}{2x(x-7)}
\\\\=
\dfrac{10+4x}{2x(x-7)}
\\\\=
\dfrac{2(5+2x)}{2x(x-7)}
\\\\=
\dfrac{\cancel{2}(5+2x)}{\cancel{2}x(x-7)}
\\\\=
\dfrac{5+2x}{x(x-7)}
.\end{array}
