Simplifying a rational expression

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The discussion focuses on simplifying the rational expression \(\frac{2(x-1)^2}{(x^2-1)^2}\) to match the book's answer \(\frac{2}{(x+1)^2}\). The key step involves recognizing that \(x^2-1\) can be factored as \((x-1)(x+1)\), which is identified as the Difference of Squares. By factoring \(x^2-1\) and simplifying the expression, the left-hand side can be reduced to the right-hand side. The participants emphasize the importance of factoring in simplifying rational expressions effectively. Understanding these algebraic manipulations is crucial for solving calculus problems accurately.
Kaylee!
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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?
 
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x2-1=(x-1)(x+1)
 
I believe it was called the Difference of Squares. Factor it out and try again.
 

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