Multiply and Divide Rational Expressions: example 8.28

Divide: $\frac{\frac{6 x^{2} - 7 x + 2}{4 x - 8}}{\frac{2 x^{2} - 7 x + 3}{x^{2} - 5 x + 6}} .$

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
$\begin{matrix} \frac{\frac{6 x^{2} - 7 x + 2}{4 x - 8}}{\frac{2 x^{2} - 7 x + 3}{x^{2} - 5 x + 6}} \\ Rewrite with a division sign. & \frac{6 x^{2} - 7 x + 2}{4 x - 8} \div \frac{2 x^{2} - 7 x + 3}{x^{2} - 5 x + 6} \\ \begin{matrix} Rewrite as product of first times \\ reciprocal of second. \end{matrix} & \frac{6 x^{2} - 7 x + 2}{4 x - 8} \cdot \frac{x^{2} - 5 x + 6}{2 x^{2} - 7 x + 3} \\ \begin{matrix} Factor the numerators and the \\ denominators, and then multiply. \end{matrix} & \frac{(2 x - 1) (3 x - 2) (x - 2) (x - 3)}{4 (x - 2) (2 x - 1) (x - 3)} \\ Simplify by dividing out common factors. & \frac{(2 x - 1) (3 x - 2) (x - 2) (x - 3)}{4 (x - 2) (2 x - 1) (x - 3)} \\ Simplify. & \frac{3 x - 2}{4} \end{matrix}$

Your turn

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

Divide: $\frac{\frac{3 x^{2} + 7 x + 2}{4 x + 24}}{\frac{3 x^{2} - 14 x - 5}{x^{2} + x - 30}} .$

How did it go?