calculus - Compute $lim_limits{xto -2^-}frac{sin(x+2)}{|4-x^2|}$ without L'Hopital's rule

Compute, without L'Hopital's rule, the limit

$$\lim_{x\to -2^-}\frac{\sin(x+2)}{|4-x^2|}$$

Since $x\to -2^-$ , the denominator can be rewritten as $-4+x^2$, but there isn't much more I've been able to do (I tried using $\sin(x+2)=\sin x\cos2+\sin2\cos x$ without getting much out of it). Thanks for your answers.