Dividing Rational Expressions

Divide the rational expressions and express the quotient in simplest form:

\frac{2 x^{2} + x - 6}{x^{2} - 1} \div \frac{x^{2} - 4}{x^{2} + 2 x + 1}

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{matrix} \frac{2 x^{2} + x - 6}{x^{2} - 1} \cdot \frac{x^{2} + 2 x + 1}{x^{2} - 4} & Rewrite as multiplication. \\ \frac{(2 x - 3) (x + 2)}{(x + 1) (x - 1)} \cdot \frac{{(x + 1)}^{2}}{(x + 2) (x - 2)} & Factor. \\ \frac{(2 x - 3) (x + 2) {(x + 1)}^{2}}{(x + 1) (x - 1) (x + 2) (x - 2)} & Multiply. \\ \frac{(2 x - 3) (x + 1)}{(x - 1) (x - 2)} & Cancel common factors to simplify. \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Divide the rational expressions and express the quotient in simplest form:

\frac{9 x^{2} - 16}{3 x^{2} + 17 x - 28} \div \frac{3 x^{2} - 2 x - 8}{x^{2} + 5 x - 14}

How did it go?