Answer
$(x-5)(x+7)$
Work Step by Step
Step 1. Factor both denominators.
$\left\{\begin{array}{ll}
x-5 & \\
x+7 &
\end{array}\right.\qquad $(already factored)
Step 2. List the factors of the first denominator.
$ List=(x-5)...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$(x+7)$ is not in the list, we add it to the list
$List=(x-5),(x+7)$
Step 4. LCD is the product of the listed factors.
$LCD=(x-5)(x+7)$
