Question

Solve: 

`((2x -3)/(x - 1)) - 4((x - 1)/(2x - 3)) = 3`

Answer 1

`((2x - 3)/(x - 1)) - 4((x - 1)/(2x - 3)) = 3`

Let `(2x -3)/(x - 1) = y`

Then `y - 4/y = 3`

`=> (y^2 - 4)/y = 3`

`=>` y² – 4 = 3y

`=>` y² – 3y – 4 = 0

`=>` y² – 4y + y – 4 = 0

`=>` y(y – 4) + 1(y – 4) = 0

`=>` (y – 4)(y + 1) = 0

If y – 4 = 0 or y + 1 = 0

Then y = 4 or y = –1

`=> (2x - 3)/(x - 1) = 4` or `(2x - 3)/(x -1) = -1`

`=>` 4x – 4 = 2x – 3 or 2x – 3 = – x + 1

`=>` 2x = 1 or 3x = 4

`=>` x = `1/2` or x = `4/3 = 1 1/3`