Answer
$\dfrac{7x-15}{x(x+1)(x-3)}$
Work Step by Step
The given expression, $
\dfrac{1}{x+1}\cdot\left( \dfrac{5}{x}+\dfrac{2}{x-3} \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{1}{x+1}\cdot\dfrac{(x-3)(5)+x(2)}{x(x-3)}
\\\\=
\dfrac{1}{x+1}\cdot\dfrac{5x-15+2x}{x(x-3)}
\\\\=
\dfrac{1}{x+1}\cdot\dfrac{7x-15}{x(x-3)}
\\\\=
\dfrac{7x-15}{x(x+1)(x-3)}
.\end{array}
