Question

Which expression is equivalent to the following complex fraction?

Answer 1

Option B

Explanation:

Numerator:

`(3)/(x -1 )-4 =(3)/(x-1)-(4*(x-1))/(x-1)\\\\`

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

Denominator:

`2-(2)/(x-1)=(2*(x-1))/(x-1)-(2)/(x-1)\\`

`= \bf (2x-2-2)/(x-1)\\\\\\= (2x-4)/(x-1)\\\\= (2*(x- 2))/(x-1)`

`((3)/(x-1)-4)/(2-(2)/(x-1))=((-4x+7)/(x-1))/((2*(x-2))/(x-1))`

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