Question

How do you solve `(2x-3) /( x-1) - (x-1 )/( x+2) = (2x-5) /( x+2) + (2-x) /( 1-x)`?

Answer 1

`x = 8/5`

Explanation:

Mutiply both sides by `(x-1)(x+2)`

`(2x-3)(x+2) - (x-1)^2 = (2x - 5)(x-1) +(x-2)(x+2)`

Simplify

`x^2 + 3x - 7 = 3x^2 - 7x + 1`
`2x^2 - 10x + 8 = 0`
`x^2 - 5x + 4 = 0`
`(x - 1)(x - 4) = 0`
`x = 1 or x = 4`

`x` must differ from `1` or we'd have a division by zero, so `x = 0`