1/(x-3)÷(x+2)/(x^2-9)-1/(x^2+5x+6)
=1/(x-3)÷(x+2)/[(x-3)(x+3)]-1/(x+2)(x+3)
=1/(x-3)*(x-3)(x+3)/(x+2)-1/(x+2)(x+3)
=(x+3)/(x+2)-[1/(x+2)-1/(x+3)]
=(x+3)/(x+2)-1/(x+2)+1/(x+3)
=(x+3-1)/(x+2)+1/(x+3)
=1+1/(x+3)
=(x+3+1)/(x+3)
=(x+4)/(x+3)