化简：(x^2+3x+9)/(x^3-27)+6/（9-x^2)-(x-1)/(6+2x)

原式=(x²+3x+9)/(x-3)(x²+3x+9)-6/(x+3)(x-3)-(x-1)/2(x+3)
=1/(x-3)-6/(x+3)(x-3)-(x-1)/2(x+3)
=(2x+6-12-x²+4x-3)/[2(x+3)(x-3)]
=-(x²-6x+9)/[2(x+3)(x-3)]
=-(x-3)²/[2(x+3)(x-3)]
=(3-x)/(2x+6)

(x^2+3x+9)/(x^3-27)+6/（9-x^2)-(x-1)/(6+2x)
=：(x^2+3x+9)/[(x-3)(x²+3x+9)]+6/（9-x^2)-(x-1)/(6+2x)
=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)]
=(2x+6-12-x²+2x+3)/[2(x+3)(x-3)]
=(-x²+4x-3)/[2(x+3)(x-3)]
=-(x-3)(x-1)/[2(x+3)(x-3)]
=-(x-1)/[2(x+3)]

(x^2+3x+9)/(x^3-27)+6/（9-x^2)-(x-1)/(6+2x)=(x^2+3x+9)/(x-3)(x²+3x+9)+6/(3-x)(3+x)-(x-1)/2(3+x)=
(12-6-2x+(x-1)(3-x))/2(3-x)(3+x)=(x+1)/2(x+3)