Problem: When simplified, (x−1+y−1)−1\left(x^{-1}+y^{-1}\right)^{-1}(x−1+y−1)−1 is equal to:
Answer Choices:
A. x+yx+yx+y
B. xyx+y\dfrac{x y}{x+y}x+yxy
C. xyx yxy
D. 1xy\dfrac{1}{x y}xy1
E. x+yxy\dfrac{x+y}{x y}xyx+y Solution:
(x−1+y−1)−1=1(1/x)+(1/y)=xyx+y\left(x^{-1}+y^{-1}\right)^{-1}=\dfrac{1}{(1 / x)+(1 / y)}=\dfrac{x y}{x+y} (x−1+y−1)−1=(1/x)+(1/y)1=x+yxy