Problem: In the expression x+1x−1\dfrac{x+1}{x-1}x−1x+1 each xxx is replaced by x+1x−1\dfrac{x+1}{x-1}x−1x+1. The resulting expression, evaluated for x=12x=\dfrac{1}{2}x=21, equals:
Answer Choices:
A. 333
B. −3-3−3
C. 111
D. −1-1−1
E. none of these Solution:
x+1x−1+1x+1x−1−1=x+1+(x−1)x+1−(x−1)=x\dfrac{\dfrac{x+1}{x-1}+1}{\dfrac{x+1}{x-1}-1}=\dfrac{x+1+(x-1)}{x+1-(x-1)}=xx−1x+1−1x−1x+1+1=x+1−(x−1)x+1+(x−1)=x