Answer
$(x-6)(x+6)$
Work Step by Step
Step 1. Factor both denominators.
The first one is already factored,
the second is a difference of squares.
$\left\{\begin{array}{lll}
(x-6) & & \\
x^{2}-36 & =x^{2}-6^{2} & =(x-6)(x+6)
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=(x-6),...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$(x-6)$ is already in the list, do not add it.
$(x+6)$ is not in the list, we add it to the list
$List=(x-6),(x+6)$
Step 4. LCD is the product of the listed factors.
$LCD=(x-6)(x+6)$
