x2-9=(x-3)(x+3); x2-3x=x(x-3); x2+3x=x(x+3). Multiply through by (x-3)(x+3):
x(x-3)(x+3)/(x2-9)-(x+4)(x-3)(x+3)/[x(x-3)]=-6(x-3)(x+3)/[x(x+3)],
which simplifies through cancellation:
x-(x+4)(x+3)/x=-6(x-3)/x, multiply through by x:
x2-(x2+7x+12)=-6x+18,
-7x-12=-6x+18,
-30=x, so x=-30.