Answer
$\displaystyle \frac{x+6}{x-6}, \qquad x\neq-6, 6$
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 sum
$=(x+6)^{2}=(x+6)(x+6)$
Denominator, factored:
$x^{2}-36$=$\quad$... recognize a differrence of squares
$=(x+6)(x-6)$
Numbers to be excluded from the domain are numbers that yield 0 in the denominator:
$x\neq-6, 6$
Expression = $\displaystyle \frac{(x+6)(x+6)}{(x+6)(x-6)}$=$\qquad$... cancel $(x+6)$
= $\displaystyle \frac{x+6}{x-6}, \qquad x\neq-6, 6$
