Упростить выражение: 1/х+1 - 2/х-2 + 3/х-1

(x-2 - 2 (x+1)) / (x-2) (x+1) + 3 / (x-1) =

= (x - 2 - 2x - 2) / (x-2) (x+1) + 3 / (x-1) =

= ((-x - 4) (x-1) + 3 (x-2) (x-1)) / (x²-1) (x-2) =

= (-x²+x-4x+4 + 3 (x²-x-2x+2)) / (x²-1) (x-2) =

= (-x²-3x+4 + 3x²-9x+6) / (x²-1) (x-2) =

= (2x²-12x+10) / (x²-1) (x-2) =

= (2 * (x-1) (x-5)) / (x-1) (x+1) (x-2) =

= (2 * (x-5)) / (x+1) (x-2) = (2x - 10) / (x+1) (x-2)