lim_(xrarr3)(1/(x^2-9)-1/(x^3-27)) =
lim_(xrarr3)(1/(x^2-3^2)-1/(x^3-3^3)) =
lim_(xrarr3)(1/((x-3)(x+3))-1/((x-3)(x^2+3x+9))) =
lim_(xrarr3)(x^2+3x+9-(x+3))/((x-3)(x+3)(x^2+3x+9)) =
lim_(xrarr3)(x^2+3x+9-x-3)/((x-3)(x+3)(x^2+3x+9)) =
lim_(xrarr3)(x^2+2x+6)/((x-3)(x+3)(x^2+3x+9))
If you replace for x=3 you get to the a/0 form
lim_(xrarr3^+)(x^2+2x+6)/((x^2-9)(x^2+3x+9)) =+oo
lim_(xrarr3^-)(x^2+2x+6)/((x^2-9)(x^2+3x+9)) =-oo