Question

50 points, question is down below.

Answer 1

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

Explanation:

The given expression to us is ,

`\implies (( 3)/(x-1) -4 )/( 2 -(2)/(x-1))`

Now take the LCM as ( x - 1 ) and Simplify , we have ,

`\implies (( 3 -4(x-1) )/(x-1) )/( (2-2(2x-1))/(x-1))`

Simplifying further , we get ,

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

Hence the second option is correct .

Answer 2

`((3)/(x-1)-4)/(2-(2)/(x-1))=\left((3)/(x-1)-(4(x-1))/(x-1)\right):\left((2(x-1))/(x-1)-(2)/(x-1)\right)\\\\=(3-4x+4)/(x-1)\cdot(2x-2-2)/(x-1)=(-4x+7)/(x-1)\cdot(x-1)/(2x-4)\\\\=(-4x+7)/(1)\cdot(1)/(2(x-2))=(-4x+7)/(2(x-2))`