Well, the numerator is always positive, right? And if x < -2, which it is, then the denominator is always negative. Since the numerator is bounded below by 4, and the denominator is going to zero, the limit is negative infinity.
The limit has the form . This is not an indeterminate form. So no special "tricks" are needed. A one sided limit in this case will always be positive or negative infinity - you just need to check which.