Answer
-1
Work Step by Step
Numerator at $x=-2:\,\,\,x^{2}+3x+2=(-2)^{2}+3(-2)+2=0$
Denominator at $x=-2:\,\,\,x+2=-2+2=0$
The function has the indeterminate form $\frac{0}{0}$ at $x=-2$.
Transforming algebraically and canceling the common factor, we have
$\frac{x^{2}+3x+2}{x+2}=\frac{(x+2)(x+1)}{x+2}=x+1$
Therefore,
$\lim\limits_{x \to -2}\frac{x^{2}+3x+2}{x+2}=\lim\limits_{x \to -2}x+1=-2+1=-1$
