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Question
Solve:
`((2x -3)/(x - 1)) - 4((x - 1)/(2x - 3)) = 3`
Solution
`((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`
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