### Home > INT3 > Chapter 11 > Lesson 11.1.2 > Problem11-20

11-20.

For each rational expression below, state any values of the variables that must be excluded (because they will make the denominator zero). Then complete each part.

1. Use the fact that $\left(x + 4\right)^{2} = \left(x + 4\right)\left(x + 4\right)$ to rewrite $\frac { ( x + 4 ) ^ { 2 } } { ( x + 4 ) ( x - 2 ) }$. Then look for $1$s and simplify.

Does anything factor out?

$x ≠ −4$ or $2$

$\frac{x+4}{x-2}$

2. Use the strategy in part (a) to simplify the expression $\frac { 8 ( x + 2 ) ^ { 3 } ( x - 3 ) ^ { 3 } } { 4 ( x + 2 ) ^ { 2 } ( x - 3 ) ^ { 5 } }$.

Does anything factor out?