Answer
$\displaystyle \frac{x-6}{4}, \qquad x\neq 6$
Work Step by Step
Numerator, factored:$\quad$
$x^{2}-12x+36$=$x^{2}-2\cdot x\cdot 6+6^{2}$=$\quad$... recognize a square of a difference
$=(x-6)^{2}=(x-6)(x-6)$
Denominator, factored:
$4x-24=4(x-6)$
Numbers to be excluded from the domain are numbers that yield 0 in the denominator:
$x\neq 6$
Expression = $\displaystyle \frac{(x-6)(x-6)}{4(x-6)}$=$\qquad$... cancel $(x-6)$
= $\displaystyle \frac{x-6}{4}, \qquad x\neq 6$
