which expression is equivalent to the following complex fraction 3/x-1 - 4 divided by 2 - 2/x-1

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

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

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

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

Respuesta :

[tex]\bf \cfrac{\quad \frac{3}{x-1}-4\quad }{2-\frac{2}{x-1}}\implies \cfrac{\quad \frac{3-4(x-1)}{x-1}\quad }{\frac{2(x-1)-2}{x-1}}\implies \cfrac{\quad \frac{3-4x+4}{x-1}\quad }{\frac{2x-2-2}{x-1}}\implies \cfrac{\quad \frac{7-4x}{x-1}\quad }{\frac{2x-4}{x-1}} \\\\\\ \cfrac{7-4x}{\underline{x-1}}\cdot \cfrac{\underline{x-1}}{2x-4}\implies \cfrac{7-4x}{2x-4}\implies \cfrac{-4x+7}{2(x-2)}[/tex]

Answer: ITS B (-4x+7/2(x-2))