(x-2)/(x^2+3x+2)+6/(2+x-x^2)-(x-10)/(x^2-4)
=(x-2)/[(x+1)(x+2)]-6/[(x+1)(x-2)]-(x-10)/[(x-2)(x+2)]
=[(x-2)^2-6(x+2)-(x-10)(x+1)]/[(x-2)(x+1)(x+2)]
=[(x^2-4x+4)-(6x+12)-(x^2-9x-10)]/[(x-2)(x+1)(x+2)]
=[-x+2]/[(x-2)(x+1)(x+2)]
=-1/[(x+1)(x+2)]