Problem:
For real numbers w and z,
w1−z1w1+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−z1w1+z1=wzz−wwzw+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