Problem: If x=1+2px=1+2^{p}x=1+2p and y=1+2−py=1+2^{-p}y=1+2−p, then yyy in terms of xxx is
Answer Choices:
A. x+1x−1\dfrac{x+1}{x-1}x−1x+1
B. x+2x−1\dfrac{x+2}{x-1}x−1x+2
C. xx−1\dfrac{x}{x-1}x−1x
D. 2−x2-\mathrm{x}2−x
E. x−1x\dfrac{x-1}{x}xx−1 Solution:
x−1=2p,y−1=2−p∴(x−1)(y−1)=1∴y=x/(x−1)x-1=2^{p}, y-1=2^{-p} \therefore(x-1)(y-1)=1 \therefore y=x /(x-1)x−1=2p,y−1=2−p∴(x−1)(y−1)=1∴y=x/(x−1).