SOLUTION: ((x)/(x+1))/((1)/(x^2-1) - (1)/(x-1))

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


   

Question 174258: ((x)/(x+1))/((1)/(x^2-1) - (1)/(x-1))
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28x%29%2F%28x%2B1%29%29%2F%28%281%29%2F%28x%5E2-1%29+-+%281%29%2F%28x-1%29%29 Start with the given expression.



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


Multiply EVERY term by the inner LCD %28x%2B1%29%28x-1%29 to clear out the inner fractions.


%28%28x-1%29x%29%2F%281-%28x%2B1%29%29 Multiply and simplify


%28x%28x-1%29%29%2F%281-%28x%2B1%29%29 Rearrange the terms.


%28x%28x-1%29%29%2F%281-x-1%29 Distribute


%28x%28x-1%29%29%2F%28-x%29 Combine like terms.


%28cross%28x%29%28x-1%29%29%2F%28-cross%28x%29%29 Cancel out the common terms.


%28x-1%29%2F%28-1%29 Simplify


-x%2B1 Reduce



So %28%28x%29%2F%28x%2B1%29%29%2F%28%281%29%2F%28x%5E2-1%29+-+%281%29%2F%28x-1%29%29 simplifies to -x%2B1


In other words, %28%28x%29%2F%28x%2B1%29%29%2F%28%281%29%2F%28x%5E2-1%29+-+%281%29%2F%28x-1%29%29=-x%2B1 where x%3C%3E-1, x%3C%3E0, or x%3C%3E1