Simplifying a rational expression

[Kaylee!]

I've done a calculus problem. The LHS is my answer and the RHS is the answer in the book.

$$\frac{2(x-1)^2}{(x^2-1)^2} = \frac{2}{(x+1)^2}$$

What was done to simplify this equation?

 

[rock.freak667]

x²-1=(x-1)(x+1)

 

[Chaos2009]

I believe it was called the Difference of Squares. Factor it out and try again.