SOLUTION: w^2-1/(w-1)^2*w-1/w^2+2w+1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: w^2-1/(w-1)^2*w-1/w^2+2w+1      Log On


   

Question 225117: w^2-1/(w-1)^2*w-1/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.


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


Break up %28w-1%29%5E2 to get %28w-1%29%28w-1%29.


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


%28%28w-1%29%2A%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,