SOLUTION: Please help me simplify this complex rational expression: 1+1/x / x-1/x one plus one over x divided by x minus 1 over x

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Question 189567: Please help me simplify this complex rational expression:
1+1/x
/
x-1/x
one plus one over x divided by x minus 1 over x

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that this is it right? %281%2B1%2Fx%29%2F%28x-1%2Fx%29


%281%2B1%2Fx%29%2F%28x-1%2Fx%29 Start with the given expression.


Multiply EVERY term by the inner LCD "x" to clear out the inner fractions.


%28x%2B1%29%2F%28x%5E2-1%29 Simplify.


%28x%2B1%29%2F%28%28x%2B1%29%28x-1%29%29 Factor the denominator (use the difference of squares formula).


highlight%28%28x%2B1%29%29%2F%28highlight%28%28x%2B1%29%29%28x-1%29%29 Highlight the common terms.


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


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



So %281%2B1%2Fx%29%2F%28x-1%2Fx%29 simplifies to 1%2F%28x-1%29


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