SOLUTION: simplify a complex fraction please. Thanks 1/9+1/3x / x/9-1/x

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Question 161797: simplify a complex fraction please. Thanks
1/9+1/3x / x/9-1/x
Answer by ankor@dixie-net.com(12692) About Me  (Show Source):
You can put this solution on YOUR website!
simplify a complex fraction
:
%281%2F9%29%2B%281%2F%283x%29%29
----------
%28x%2F9%29-%281%2Fx%29
:
Convert both to a single fraction over a common denominator
%28%28x%2B3%29%29%2F%289x%29
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%28x%28x%29-9%281%29%29%2F%289x%29
:
which is:
%28%28x%2B3%29%29%2F%289x%29
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%28%28x%5E2-9%29%29%2F%289x%29
:
Invert the dividing fraction and multiply, cancel out 9x
%28%28x%2B3%29%29%2F%289x%29 * %289x%29%2F%28%28x%5E2-9%29%29 = %28%28x%2B3%29%29%2F%28%28x%5E2-9%29%29
:
Note that x^2-9 is the "difference of squares" so factor that. Cancel out x+3
%28%28x%2B3%29%29%2F%28%28x%2B3%29%28x-3%29%29 = 1%2F%28%28x-3%29%29