The bottoms of the fractions are x^2 - 1, (x-1)^2, and x^2
x^2 - 1 = (x+1)(x-1)
(x-1)^2 = (x-1)(x-1)
x^2 = x * x
It's like we're making a parts list with enough parts to make x^2 - 1 or (x-1)^2 or x^2. In this case our parts list is x x * x *(x-1) * (x-1) * (x+1) because that list has enough parts to make x^2 - 1 or (x-1)^2 or x^2.
x * x * (x-1) * (x-1) * (x+1) = x^2 (x-1)^2 (x+1)
Answer: The LCD is x^2 (x-1)^2 (x+1)