Problem:
For real numbers w and z,
w1​−z1​w1​+z1​​=2014
What is w−zw+z​?
Answer Choices:
A. −2014
B. 2014−1​
C. 20141​
D. 1
E. 2014
Solution:
Note that
2014=w1​−z1​w1​+z1​​=wzz−w​wzw+z​​=z−ww+z​
Because z−ww+z​=−w−zw+z​, the requested value is (A)−2014​.
The problems on this page are the property of the MAA's American Mathematics Competitions