1/(x+1)-(x-3)/(x²-1)×(x²-2x+1)/[(x-1)(x-3)]
=1/(x+1)-(x-3)/[(x+1)(x-1)]×(x-1)²/[(x-1)(x-3)]
=1/(x+1)-(x-3)/(x+1)×1/(x-3)
=1/(x+1)-1/[(x+1)
=0