Question

Which expression is equivalent to the following complex fraction? (pls help me out)​

Answer 1

Answer:

B. $\frac{-4x + 7}{2(x - 2)}$

Step-by-step explanation:

Simplify the given expression to determine its equivalent expression in the given options.

$\frac{\frac{3}{x - 1} - 4}{2 - \frac{2}{x - 1}}$

$\frac{\frac{3}{x - 1} - \frac{4}{1}}{\frac{2}{1} - \frac{2}{x - 1}}$

$\frac{\frac{3 - 4(x - 1)}{x - 1}}{\frac{2(x - 1) - 2}{x - 1}}$

$\frac{\frac{3 - 4x + 4}{x - 1}}{\frac{2x - 2 - 2}{x - 1}}$

$\frac{\frac{-4x + 7}{x - 1}}{\frac{2x - 4}{x - 1}}$

$\frac{-4x + 7}{x - 1} * \frac{x - 1}{2x - 4}$

(x - 1) cancels (x - 1)

$\frac{-4x + 7}{1} * \frac{1}{2x - 4}$

$\frac{(-4x + 7)1}{1(2x - 4)}$

$\frac{-4x + 7}{2x - 4}$

$\frac{-4x + 7}{2(x - 2)}$