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(xyy+xyx)=x+y1(xyx+y)=(x+y)1⋅xy(x+y)=xy1=x−1y−1