SOLUTION: Perform the operation w^2 - 1 over (w - 1)^2 * w - 1 over w^2 + 2w + 1

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Question 199987: Perform the operation
w^2 - 1 over (w - 1)^2 * w - 1 over w^2 + 2w + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28%28w%5E2-1%29%2F%28%28w-1%29%5E2%29%29%28%28w-1%29%2F%28w%5E2%2B2w%2B1%29%29 Start with the given expression.


%28%28%28w-1%29%28w%2B1%29%29%2F%28%28w-1%29%5E2%29%29%28%28w-1%29%2F%28w%5E2%2B2w%2B1%29%29 Factor w%5E2-1 to get %28w-1%29%2A%28w%2B1%29.


Factor %28w-1%29%5E2 to get %28w-1%29%28w-1%29.


Factor w-1 to get 1%28w-1%29.


Factor w%5E2%2B2w%2B1 to get %28w%2B1%29%28w%2B1%29.


%28%28w-1%29%28w%2B1%29%28w-1%29%29%2F%28%28w-1%29%28w-1%29%28w%2B1%29%28w%2B1%29%29 Combine the fractions.


Highlight the common terms.


Cancel out the common terms.


1%2F%28w%2B1%29 Simplify.


So %28%28w%5E2-1%29%2F%28%28w-1%29%5E2%29%29%28%28w-1%29%2F%28w%5E2%2B2w%2B1%29%29 simplifies to 1%2F%28w%2B1%29.


In other words, where w%3C%3E-1 or w%3C%3E1