Answer
$\displaystyle \frac{x-4}{3}, \qquad x\neq 4$
Work Step by Step
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 $(x-4)$
= $\displaystyle \frac{x-4}{3}, \qquad x\neq 4$
