Answer
$\dfrac{9x^{5}}{a^{2}-b^{2}}\div\dfrac{27x^{2}}{3b-3a}=-\dfrac{x^{3}}{a+b}$
Work Step by Step
$\dfrac{9x^{5}}{a^{2}-b^{2}}\div\dfrac{27x^{2}}{3b-3a}$
Factor the denominator of the first fraction and take out common factor $3$ from the denominator of the second fraction:
$\dfrac{9x^{5}}{a^{2}-b^{2}}\div\dfrac{27x^{2}}{3b-3a}=\dfrac{9x^{5}}{(a-b)(a+b)}\div\dfrac{27x^{2}}{3(b-a)}=...$
Evaluate the division of the two rational expressions:
$...=\dfrac{27x^{5}(b-a)}{27x^{2}(a-b)(a+b)}=...$
Simplify by removing repeated factors in the numerator and the denominator. To do that, let's change the sign of the numerator and the sign of the fraction:
$...=\dfrac{x^{3}(b-a)}{(a-b)(a+b)}=-\dfrac{-x^{3}(b-a)}{(a-b)(a+b)}=-\dfrac{x^{3}(a-b)}{(a-b)(a+b)}=...$
$...=-\dfrac{x^{3}}{a+b}$
