Problem:
If x−1x=y2+2y−2y2+2y−1, then x equals
Answer Choices:
A. y2+2y−1
B. y2+2y−2
C. y2+2y+2
D. y2+2y+1
E. −y2−2y+1
Solution:
(y2+2y−2)x[(y2+2y−2)−(y2+2y−1)]xx=(y2+2y−1)x−(y2+2y−1)=−(y2+2y−1)=y2+2y−1.
OR
Rewrite the right member of the given equality as (y2+2y−1)−1(y2+2y−1) and note by inspection that x=y2+2y−1.