### Home > AC > Chapter 10 > Lesson 10.1.1 > Problem10-10

10-10.

For each rational expression below, state any values of the variables that would make the denominator zero. Then complete each part.

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

For the denominator to equal zero $(x+4)(x-2)$ must equal zero.

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

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

What values of $x$ would make the denominator zero?

Rewrite the expression, as shown below, and look for factors which simplify to one.

$\frac{8(x+2)(x+2)(x+2)(x-3)(x-3)(x-3)}{4(x+2)(x+2)(x-3)(x-3)(x-3)(x-3)(x-3)}$