Answer
$-1$
Work Step by Step
With $x\to -4^-$, we have $x+4\lt0$ and $|x+4|=-x-4$. Thus
$$\lim_{x\to -4^-}\frac{|x+4|}{x+4}=\frac{\lim_{x\to -4^-}|x+4|}{\lim_{x\to -4^-}x+4}=\frac{-x-4}{x+4}=-1$$
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