Question

Which expression is equivalent to the following complex fraction?

Answer 1

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)

Answer 2

Answer:

-4x+7/2(x-2)

Step-by-step explanation:

On edgen Option B is correct.