Answer
$(y+1)(y-1)^{2}$
Work Step by Step
Step 1. Factor both denominators.
The first one is a difference of squares,
the second is is a square of a difference.
$\left\{\begin{array}{lll}
y^{2}-1 & =y^{2}-1^{2} & =(y+1)(y-1)\\
y^{2}-2y+1 & =(y-1)^{2} & =(y-1)(y-1)
\end{array}\right.$
Step 2. List the factors of the first denominator.
$ List=(y+1),(y-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.
One of the two factors $(y-1)$ is in the list, we add the other one to the list
$List=(y+1),(y-1),(y-1),...$
Step 4. LCD is the product of the listed factors.
$LCD=(y+1)(y-1)(y-1)$
or
$(y+1)(y-1)^{2}$
