Question

In the following exercises, multiply.

$\frac{18c-2c^2}{6c+30}·\frac{c^2+7c+10}{c^2-81}$

Short answer

The required answer is$-\frac{c\left(c+2\right)}{3\left(c+9\right)}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

$\frac{18c-2c^2}{6c+30}·\frac{c^2+7c+10}{c^2-81}$

Step 2. Simplify the expression.

$\frac{18c-2c^2}{6c+30}·\frac{c^2+7c+10}{c^2-81}$

Factor the numerator and denominator completely,

$\frac{2c\left(9-c\right)}{6\left(c+5\right)}·\frac{\left(c+5\right)\left(c+2\right)}{\left(c+9\right)\left(c-9\right)}$

Multiply the numerators and denominators,

$-\frac{2c\left(c-9\right)\left(c+5\right)\left(c+2\right)}{6\left(c+5\right)\left(c+9\right)\left(c-9\right)}$

Simplify by dividing out common factors,

$-\frac{c\left(c+2\right)}{3\left(c+9\right)}$