Answer: the second option is the correct answer
Step-by-step explanation:
The given expression is
[3/(x - 1) - 4]/[2 - 2/(x - 1)
We would simplify the numerator first. The LCM of the numerator is
x - 1. Taking the LCM of the numerator, it becomes
[3 - 4(x - 1)]/(x - 1)
= [3 - 4x + 4]/(x - 1)
= (- 4x + 7)/(x - 1)
We would simplify the denominator. The LCM of the denominator is
x - 1. Taking the LCM of the numerator, it becomes
[2(x - 1) - 2]/(x - 1)
= [2x - 2 - 2]/(x - 1)
= (2x - 4)/(x - 1)
= 2(x - 2)/(x - 1)
The expression becomes
[(- 4x + 7)/(x - 1)]/[ 2(x - 2)/(x - 1)]
= (- 4x + 7)/(x - 1) × (x - 1)/2(x - 2)
(x - 1) cancels out. It becomes
(- 4x + 7) / 2(x - 2)
