Answer
At $-1$: $1$.
The domain is all real numbers except $-2$.
Work Step by Step
We plug in $x=-1$ to $f(x)$ to get $f(-1)=\frac{-1+2}{|-1+2|}=\frac{1}{|1|}=\frac{1}{1}=1.$
We know that the denominator cannot be $0$, hence $|x+2|\ne0\\x+2\ne0\\x\ne-2.$
Thus the domain is all real numbers except $-2$.
