(x^2+9)/(x^2+3x)-(x^2-9)/(x^2-6x+9)
=(x^2+9)/(x^2+3x)-(x-3)(x+3)/(x-3)^2
=(x^2+9)/x(x+3)-(x+3)/(x-3)
=(x^2+9)(x-3)/x(x+3)(x-3)-x(x+3)^2/x(x+3)(x-3)
=[(x^2+9)(x-3)-x(x+3)^2]/x(x+3)(x-3)
=[(x^3-3x^2+9x-27)-x(x^2+6x+9)]/x(x+3)(x-3)
=(x^3-3x^2+9x-27-x^3-6x^2-9x)/x(x+3)(x-3)
=(x^3-x^3-6x^2-3x^2+9x-9x-27)/x(x+3)(x-3)
=(-9x^2-27)/x(x+3)(x-3)
=-9(x^2+3)/x(x+3)(x-3)