Chapter 6, Problem 18AR

To determine

To simplify the fraction $\frac{a^2+8a+16}{a^2-16}$ .

Answer to Problem 18AR

  $\frac{a^2+8a+16}{a^2-16}=\frac{a+4}{a-4}$

Explanation of Solution

Given:

  $\frac{a^2+8a+16}{a^2-16}$

Calculation:

The fraction can be simplified as

  $\begin{array}{l}\frac{a^2+8a+16}{a^2-16}=\frac{a^2+4a+4a+16}{a^2-4^2}\\ =\frac{a\left(a+4\right)+4\left(a+4\right)}{\left(a+4\right)\left(a-4\right)}\\ =\frac{\left(a+4\right)\left(a+4\right)}{\left(a+4\right)\left(a-4\right)}\\ =\frac{a+4}{a-4}\end{array}$