SOLUTION: how do you simplify x-1/x^2+2x+1(.)x^2-1/(x-1)^2

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Question 243102: how do you simplify
x-1/x^2+2x+1(.)x^2-1/(x-1)^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x-1%29%2F%28x%5E2%2B2x%2B1%29%29%28%28x%5E2-1%29%2F%28%28x-1%29%5E2%29%29 Start with the given expression.


%28%28%28x-1%29%29%2F%28x%5E2%2B2x%2B1%29%29%28%28x%5E2-1%29%2F%28%28x-1%29%5E2%29%29 Factor x-1 to get %28x-1%29.


Factor x%5E2%2B2x%2B1 to get %28x%2B1%29%28x%2B1%29.


Factor x%5E2-1 to get %28x-1%29%2A%28x%2B1%29.


Expand %28x-1%29%5E2 to get %28x-1%29%28x-1%29.


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


Highlight the common terms.


Cancel out the common terms.


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


So %28%28x-1%29%2F%28x%5E2%2B2x%2B1%29%29%28%28x%5E2-1%29%2F%28%28x-1%29%5E2%29%29 simplifies to 1%2F%28x%2B1%29.


In other words,