Question

Which expression is equivalent to the following complex fraction?

Answer 1

Answer:

Option B

Step-by-step explanation:

Numerator:

$\dfrac{3}{x -1 }-4 =\dfrac{3}{x-1}-\dfrac{4*(x-1)}{x-1}$

                 $=\dfrac{3- 4x -4*(-1)}{x-1}=\dfrac{3-4x+4}{x-1}\\\\\\=\dfrac{-4x+7}{x-1} \: \textbf{ [Combine like terms]}$

Denominator:

$2-\dfrac{2}{x-1}=\dfrac{2*(x-1)}{x-1}-\dfrac{2}{x-1}$

                $= \bf \dfrac{2x-2-2}{x-1}\\\\\\= \dfrac{2x-4}{x-1}\\\\= \dfrac{2*(x- 2)}{x-1}$

$\dfrac{\dfrac{3}{x-1}-4}{2-\dfrac{2}{x-1}}=\dfrac{\dfrac{-4x+7}{x-1}}{\dfrac{2*(x-2)}{x-1}}$

                 $\bf = \dfrac{-4x+7}{x-1}*\dfrac{x-1}{2(x-2)} \ \ \ \textbf{ [(x-1) in the numerator and denominator will be cancelled]}\\\\\\=\dfrac{-4x+7}{2(x-2)}$