Problem: When simplified and expressed with negative exponents, the expression (x+y)−1(x−1+y−1) is equal to:
Answer Choices:
A. x−2+2x−1y−1+y−2
B. x−2+2−1x−1y−1+y−2
C. x−1y−1
D. x−2+y−2
E. x−1y−11​
Solution:
(x+y)−1(x−1+y−1)=x+y1​(x1​+y1​)=x+y1​⋅xyx+y​=xy1​=x−1y−1.