SOLUTION: (x^-1+y^-1)^-1 I am unsure of how I am supposed to finish this problem. I flipped it becaues of the negative exponent and ended up with x^-1+y^-1/1 and then flipped it again bec

Algebra ->  Exponents -> SOLUTION: (x^-1+y^-1)^-1 I am unsure of how I am supposed to finish this problem. I flipped it becaues of the negative exponent and ended up with x^-1+y^-1/1 and then flipped it again bec      Log On


   

Question 749119: (x^-1+y^-1)^-1
I am unsure of how I am supposed to finish this problem. I flipped it becaues of the negative exponent and ended up with x^-1+y^-1/1 and then flipped it again because of the negative exponents on x and y. And ended up with 1/2x and 1/2y. I Don't recall in our lesson seeing problems with negative exponents on the inside and outside so I just figured you would keep flipping them til they were gone. I have a feeling that is incorrect.
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E-1%2By%5E-1%29%5E-1=1%2F%28x%5E-1%2By%5E-1%29=1%2F%28%281%2Fx%29%2B%281%2Fy%29%29

At the lower level, focus on the main denominator. Lowest Common Denominator of the main denominator is xy. Try this: Multiply the whole complex fraction by %28xy%29%2F%28xy%29. That should give you something which simplifies neatly into a noncomplex fraction.

%281%2F%28%281%2Fx%29%2B%281%2Fy%29%29%29%2A%28%28xy%29%2F%28xy%29%29
xy%2F%28xy%2Fx%2Bxy%2Fy%29
highlight%28xy%2F%28y%2Bx%29%29