SOLUTION: Simplify the complex fraction. Assume no division by 0. 1/x + 7/(x+1) divided by 7/(x-1) - 1/x

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Question 1129164: Simplify the complex fraction. Assume no division by 0.
1/x + 7/(x+1) divided by 7/(x-1) - 1/x
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2Fx+%2B+7%2F%28x%2B1%29%29%2F%287%2F%28x-1%29+-+1%2Fx%29
The least common denominator of all three fractions, top and bottom, is x%2A%28x%2B1%29%2A%28x-1%29, so
multiply every term in numerator and denominator by %28%28x%2A%28x%2B1%29%2A%28x-1%29%29%2F1%29:





 

 

%28+%28x%5E2-1%29+%2B+%287x%5E2-7x%29++%29%2F%28+%287x%5E2%2B7x%29-+%28x%5E2-1%29+%29%29

%28+x%5E2-1+%2B+7x%5E2-7x++%29%2F%28+7x%5E2%2B7x-+x%5E2%2B1+%29%29

%288x%5E2+-+7x+-+1%29%2F%286x%5E2+%2B+7x+%2B+1%29

We can factor the numerator and the denominator:

%28%288x+%2B+1%29+%28x+-+1%29%29%2F%28%286x+%2B+1%29%28x+%2B+1%29%29

But nothing cancels.

Edwin