## Algebra: A Combined Approach (4th Edition)

$\dfrac{9x^{5}}{a^{2}-b^{2}}\div\dfrac{27x^{2}}{3b-3a}=-\dfrac{x^{3}}{a+b}$
$\dfrac{9x^{5}}{a^{2}-b^{2}}\div\dfrac{27x^{2}}{3b-3a}$ 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: $...=\dfrac{x^{3}(b-a)}{(a-b)(a+b)}=-\dfrac{-x^{3}(b-a)}{(a-b)(a+b)}=-\dfrac{x^{3}(a-b)}{(a-b)(a+b)}=...$ $...=-\dfrac{x^{3}}{a+b}$