Question

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

Answer 1

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

Answer 2

`\bf \cfrac{\quad (3)/(x-1)-4\quad }{2-(2)/(x-1)}\implies \cfrac{\quad (3-4(x-1))/(x-1)\quad }{(2(x-1)-2)/(x-1)}\implies \cfrac{\quad (3-4x+4)/(x-1)\quad }{(2x-2-2)/(x-1)}\implies \cfrac{\quad (7-4x)/(x-1)\quad }{(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)}`