Problem:
Which of the following is equivalent to
1−xx−1​x​​
when x<0?
Answer Choices:
A. −x
B. x
C. 1
D. 2x​​
E. x−1​
Solution:
We have
1−xx−1​x​​=xx−x+1​x​​=x1​x​​=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