Problem:
1−21​1−31​​=
Answer Choices:
A. 31​
B. 32​
C. 43​
D. 23​
E. 34​
Solution:
1−21​1−31​​=21​32​​=32​×12​=34​.
OR
Multiplying both numerator and denominator by 6 yields
6(1−21​)6(1−31​)​=6−36−2​=34​.
Answer: E​.
The problems on this page are the property of the MAA's American Mathematics Competitions