Answer
$\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}=\dfrac{3x+1}{5x+1}$
Work Step by Step
$\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}$
Factor both rational expressions completely:
$\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}=\dfrac{x^{2}(x+7)}{x^{2}(3x-1)}\div\dfrac{(x+7)(5x+1)}{(3x-1)(3x+1)}$
Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expressions:
$...=\dfrac{x^{2}(x+7)(3x-1)(3x+1)}{x^{2}(3x-1)(x+7)(5x+1)}=\dfrac{3x+1}{5x+1}$
