Question

In the following exercises, divide the rational expressions.

$\frac{{\displaystyle \frac{3b^2+2b-8}{12b+18}}}{{\displaystyle \frac{3b^2+2b-8}{2b^2-7b-15}}}$

Short answer

The simplified expression is$\frac{\left(b-5\right)}{6}.$

Step-by-step solution

Step 1. Given Information

$=\frac{3b^2+2b-8}{12b+18}÷\frac{3b^2+2b-8}{2b^2-7b-15}$

Step 2. Rewrite as product of first times reciprocalof second.

$\frac{3b^2+2b-8}{12b+18}\times \frac{2b^2-7b-15}{3b^2+2b-8}$

Step 3. Factor the numerators and thedenominators, and then multiply.

$$\begin{gathered} \frac{3b^2+2b-8}{12b+18}\times \frac{2b^2-7b-15}{3b^2+2b-8} \\ =\frac{2b^2-7b-15}{12b+18}=\frac{\left(b-5\right)\left(2b+3\right)}{6\left(2b+3\right)} \end{gathered}$$

Step 4. Simplify by dividing out common factors.

$\frac{b-5}{6}.$