[tex]\lim\limits_{x\to -1}\dfrac{x^2-1}{x^2+3x+2} = \lim\limits_{x\to -1}\dfrac{(x-1)(x+1)}{(x+1)(x+2)} = \\ \\ = \lim\limits_{x\to -1}\dfrac{x-1}{x+2}= \dfrac{-1-1}{-1+2} = \dfrac{-2}{1} = \boxed{-2}[/tex]
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