## Precalculus (6th Edition) Blitzer

$\displaystyle \frac{x-4}{3}, \qquad x\neq 4$
Numerator, factored:$\quad$ $x^{2}-12x+36$=$x^{2}-2\cdot x\cdot 4+4^{2}$=$\quad$... recognize a square of a difference $=(x-4)^{2}=(x-4)(x-4)$ Denominator, factored: $3x-12=3(x-4)$ Numbers to be excluded from the domain are numbers that yield 0 in the denominator: $x\neq 4$ Expression = $\displaystyle \frac{(x-4)(x-4)}{3(x-4)}$=$\qquad$... cancel $(x-4)$ = $\displaystyle \frac{x-4}{3}, \qquad x\neq 4$