Problem: The equality 1x−1=2x−2\dfrac{1}{x-1}=\dfrac{2}{x-2}x−11=x−22 is satisfied by:
Answer Choices:
A. no real values of xxx
B. either x=1x=1x=1 or x=2x=2x=2
C. only x=1x=1x=1
D. only x=2x=2x=2
E. only x=0x=0x=0 Solution:
Multiplying both sides of the equation by (x−1)(x−2)(x-1)(x-2)(x−1)(x−2), we have 2x−2=x−2.∴x=02 x-2=x-2 . \quad \therefore x=02x−2=x−2.∴x=0.