SOLUTION: Please help to simplify (1/x+1/y)/(1/x-1/y) Please show detailed workings thank you.

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Question 991924: Please help to simplify (1/x+1/y)/(1/x-1/y)
Please show detailed workings thank you.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Lowest or simplest common denominator is xy, so multiply the complex fraction by 1=%28xy%29%2F%28xy%29.

%28%281%2Fx%2B1%2Fy%29%2F%281%2Fx-1%2Fy%29%29%28%28xy%29%2F%28xy%29%29

%28y%2Bx%29%2F%28y-x%29

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
1%2Fx + 1%2Fy = y%2F%28xy%29 + x%2F%28xy%29 = %28y%2Bx%29%2F%28xy%29.

1%2Fx - 1%2Fy = y%2F%28xy%29 - x%2F%28xy%29 = %28y-x%29%2F%28xy%29.

Therefore,

%281%2Fx+%2B+1%2Fy%29%2F%281%2Fx+-+1%2Fy%29 = %28%28y%2Bx%29%2F%28xy%29%29%2F%28%28y-x%29%2F%28xy%29%29 = %28%28y%2Bx%29%2A%28xy%29%29%2F%28%28y-x%29%2A%28xy%29%29 = %28y%2Bx%29%2F%28y-x%29.