Problem:
Which of the following is equivalent to
1−xx−1x
when x<0?
Answer Choices:
A. −x
B. x
C. 1
D. 2x
E. x−1
Solution:
We have
1−xx−1x=xx−x+1x=x1x=x2=∣x∣
When x<0, the given expression is equivalent to (A)−x.
The problems on this page are the property of the MAA's American Mathematics Competitions