SOLUTION: How would you simplify (1+(1/x))/(1-(1/x^2))?

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Question 198378: How would you simplify (1+(1/x))/(1-(1/x^2))?
Found 2 solutions by jim_thompson5910, arallie:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B%281%2Fx%29%29%2F%281-%281%2Fx%5E2%29%29 Start with the given expression.


Multiply EVERY term by the inner LCD x%5E2 to clear out the inner fractions.


%28x%5E2%2Bx%29%2F%28x%5E2-1%29 Simplify


%28x%28x%2B1%29%29%2F%28x%5E2-1%29 Factor the numerator


%28x%28x%2B1%29%29%2F%28%28x%2B1%29%28x-1%29%29 Factor the denominator


%28x%2Across%28%28x%2B1%29%29%29%2F%28cross%28%28x%2B1%29%29%28x-1%29%29 Cancel out the common terms.


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


So %281%2B%281%2Fx%29%29%2F%281-%281%2Fx%5E2%29%29=x%2F%28x-1%29

Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B%281%2Fx%29%29%2F%281-%281%2Fx%5E2%29%29
Mult top and bottom by x^2
%28x%5E2%29%281%2B%281%2Fx%29%29%2F%28x%5E2%29%281-%281%2Fx%5E2%29%29
%28x%5E2%2Bx%29%2F%28x%5E2-1%29
Factor
%28x%29%28x%2B1%29%2F%28x%2B1%29%28x-1%29
Simplify
x%2F%28x-1%29