Answer
$\dfrac{x^3}{3(x+1)}$
Work Step by Step
The given expression, $
\dfrac{\dfrac{x^2}{15}}{\dfrac{x+1}{5x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{x^2}{15}\div\dfrac{x+1}{5x}
\\\\=
\dfrac{x^2}{15}\cdot\dfrac{5x}{x+1}
\\\\=
\dfrac{x^2}{\cancel{5}\cdot3}\cdot\dfrac{\cancel{5}x}{x+1}
\\\\=
\dfrac{x^3}{3(x+1)}
.\end{array}
