Question

In the following exercises, multiply.

$\frac{72m-12m^2}{8m+32}·\frac{m^2+10m+24}{m^2-36}$

Short answer

The required answer is$-\frac{3m}{2}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{72m-12m^2}{8m+32}·\frac{m^2+10m+24}{m^2-36}$

Step 2. Simplify the expression.

$\frac{72m-12m^2}{8m+32}·\frac{m^2+10m+24}{m^2-36}$

Factor the numerator and denominator completely,

role="math" localid="1647950564175" $\frac{12m\left(6-m\right)}{8\left(m+4\right)}·\frac{\left(m+6\right)\left(m+4\right)}{\left(m+6\right)\left(m-6\right)}$

Multiply the numerators and denominators,

$-\frac{4·3·m\left(m-6\right)\left(m+6\right)\left(m+4\right)}{4·2\left(m+4\right)\left(m+6\right)\left(m-6\right)}$

Simplify by dividing out common factors,

$-\frac{3m}{2}$