This works out beautifully. You COULD use long division here, but since your numerator is a quadratic, your first instinct should be to try and factor it. If you factor it, it works out to be (x - 3)(x + 2). Now it just so happens that when you do that, the (x - 3) in the numerator will cancel with the (x - 3) in the denominator leaving you with one sad and lonely (x + 2) as your answer.
