Answer
$x^{2}(x+1)$
Work Step by Step
We switch from division to multiplication by taking the reciprocal of the bottom fraction. Then we factor and simplify:
$\displaystyle\frac{\frac{x^{3}}{x+1}}{\frac{x}{x^{2}+2x+1}}=\frac{x^{3}}{x+1}.\frac{x^{2}+2x+1}{x}=\frac{x^{3}(x+1)(x+1)}{(x+1)x}=x^{2}(x+1)$
