Question

Which expression is equivalent to the following complex fraction?

(3/x-1 - 4) / (2 - 2/x-1)

a. 2(x-2)/-4x+7
b. -4x+7/2(x-2)
c. -4x+7/2(x²-2)
d. 2(x²-2)/-4x+7

Answer 1

The expression (-4x + 7)/(2x - 4) is equivalent to the given complex fraction. So, the correct answer is option a.

Step-by-step explanation:

To simplify the complex fraction, we can start by simplifying the expressions in the numerator and denominator separately. Simplifying the numerator, we have:

3/(x - 1) - 4 = (3 - 4(x - 1))/(x - 1) = (3 - 4x + 4)/(x - 1) = (-4x + 7)/(x - 1)

Simplifying the denominator, we have:

2 - 2/(x - 1) = (2(x - 1) - 2)/(x - 1) = (2x - 2 - 2)/(x - 1) = (2x - 4)/(x - 1)

Combining the simplified numerator and denominator, we get the equivalent expression:

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