Problem:
Consider the operation "minus the reciprocal" of, defined by a⋄b=a−b1​. What is ((1⋄2)⋄3)−(1⋄(2⋄3))?
Answer Choices:
A. −307​
B. −61​
C. 0
D. 61​
E. 307​
Solution:
((1⋄2)⋄3)−(1⋄(2⋄3))​=((1−21​)−31​)−(1−(2−31​)−1)=61​−(1−53​)=61​−52​=(A)−307​​​
The problems on this page are the property of the MAA's American Mathematics Competitions