Chapter 8.1, Problem 23PPS

To determine

Simplify the given expression.

Answer to Problem 23PPS

The required simplified expression is $-\frac{c+4}{c+5}$ .

Explanation of Solution

Given information: Given the expression is $\frac{16-c^2}{c^2+c-20}$ .

Calculation:

Given the expression:

  $\begin{array}{l}\frac{16-c^2}{c^2+c-20}\\ =\frac{\left(4-c\right)\left(4+c\right)}{c^2+5c-4c-20}\text{ factor }\\ =\frac{\left(4-c\right)\left(4+c\right)}{c\left(c+5\right)-4\left(c+5\right)}\text{ factor }\\ =\frac{-\left(c-4\right)\left(4+c\right)}{\left(c+5\right)\left(c-4\right)}\text{ factor }\\ =\frac{-\left(c-4\right)\left(c+4\right)}{\left(c+5\right)\left(c-4\right)}\\ =-\frac{c+4}{c+5}\text{ like terms cancel out}\end{array}$

Thus, the required simplified expression is $-\frac{c+4}{c+5}$