## Precalculus (6th Edition) Blitzer

$=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$
Factor what you can: $6x+9=3(2x+3)$ $3x-15=3(x-5)$ $x-5$ is factored $4x+6=2(2x+3)$ Expression $=\displaystyle \frac{3(2x+3)}{3(x-5)}\cdot\frac{(x-5)}{2(2x+3)}\qquad$ ...exclude the values that yield 0 in the denominator: $x\displaystyle \neq 5,-\frac{3}{2}$ ... cancel common factors: $3,\ (x-5)$, and $(2x+3)$ $=\displaystyle \frac{1}{2},\qquad x\displaystyle \neq 5,-\frac{3}{2}$