(1/x+1)*[(x-3/x^2+6x+9)+(2/3+x)]-(x/x^2-9)

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