Answer
$\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}=\dfrac{3(x+1)}{x^{3}(x-1)}$
Work Step by Step
$\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}$
Factor the denominator of the first fraction:
$\dfrac{3x^{2}}{x^{2}-1}\div\dfrac{x^{5}}{(x+1)^{2}}=\dfrac{3x^{2}}{(x-1)(x+1)}\div\dfrac{x^{5}}{(x+1)^{2}}=...$
Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator:
$...=\dfrac{3x^{2}(x+1)^{2}}{x^{5}(x-1)(x+1)}=\dfrac{3x^{2}(x+1)}{x^{5}(x-1)}=\dfrac{3(x+1)}{x^{3}(x-1)}$
