Question

Which expression is equivalent to the following complex fraction?

StartFraction 3 Over x minus 1 EndFraction minus 4 divided by 2 minus StartFraction 2 Over x minus 1 EndFraction
StartFraction 2 (x minus 2) Over negative 4 x + 7 EndFraction
StartFraction negative 4 x + 7 Over 2 (x minus 2) EndFraction
StartFraction negative 4 x + 7 Over 2 (x squared minus 2) EndFraction
StartFraction 2 (x squared minus 2) Over (negative 4 x + 7) EndFraction

Answer 1

B

Explanation:

I got it right on EDGE

Answer 2

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

Explanation:

The first step is to combine the parts of the numerator and denominator into one rational expression each. Those will have the same denominator, so their ratio is the ratio of their numerators.

`((3)/(x-1)-4)/(2-(2)/(x-1))=(\left((3-4(x-1))/(x-1)\right))/(\left((2(x-1)-2)/(x-1)\right))=(3-4(x-1))/(2(x-1)-2)\\\\=(3-4x+4)/(2x-2-2)=\boxed{(-4x+7)/(2(x-2))}`