Problem: If the reciprocal of x+1x+1x+1 is x−1x-1x−1, then xxx equals:
Answer Choices:
A. 000
B. 111
C. −1-1−1
D. +1 or -1
E. none of these Solution:
Since 1x+1=x−1,x2−1=1,x2=2,x=+2\dfrac{1}{x+1}=x-1, x^{2}-1=1, x^{2}=2, x=+\sqrt{2}x+11=x−1,x2−1=1,x2=2,x=+2 or −2-\sqrt{2}−2 \quad