Answer
$(x-6)(x+1)(x-5)$
Work Step by Step
Step 1. Factor both denominators.
The first one is a trinomial $x^{2}+bx+c.$
... We find factors of $c=-6$ whose sum is $b=-5$.
... these are $-6$ and $+1$.
$x^{2}-5x-6=(x-6)(x+1)$
The second one is also a trinomial $x^{2}+bx+c.$
... We find factors of $c=-5$ whose sum is $b=-4$.
... these are $-5$ and $+1$.
$x^{2}-4x-5=(x-5)(x+1)$
Step 2. List the factors of the first denominator.
$ List=(x-6),(x+1),...\qquad$ (list in progress)
Step 3. Add to the list in step 2 any factors of the second denominator that are not yet listed.
$(x-5)$ is not in the list, we add it to the list
$List=(x-6),(x+1),(x-5),...$
$(x+1)$ is already in the list - do not add it to the list.
Step 4. LCD is the product of the listed factors.
$LCD=(x-6)(x+1)(x-5)$
