(x²+3x+9)/(x³-27)+6/(9-x²)-(x-1)/(6+2x)
=(x²+3x+9)/[(x-3)(x²+3x+9)]-6/(x²-9)-(x-1)/[2(x+3)]
=1/(x-3)-6/[(x+3)(x-3)]-(x-1)/[2(x+3)]
=[2(x+3)-12-(x-1)(x-3)]/[2(x+3)(x-3)]
=-(x²-6x+9)/[2(x+3)(x-3)]
=-(x-3)²/[2(x-3)(x+3)]
=-(x-3)/2(x+3)