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**Siron** The importance of plugging in -2 first is that you can determine if you're dealing with an undetermined form or not, in this case you see you get the undetermined form: $\displaystyle \frac{0}{0}$.

Calculating:

$\displaystyle \lim_{x \to -2} \frac{(x+2)\cdot (\sqrt{x^2+5}+3)}{(\sqrt{x^2+5}-3)\cdot (\sqrt{x^2+5}+3)}$

$\displaystyle =\lim_{x \to -2} \frac{(x+2)\cdot (\sqrt{x^2+5}+3)}{x^2-4}$

$\displaystyle =\lim_{x\to -2} \frac{(x+2)\cdot (\sqrt{x^2+5}+3)}{(x-2)\cdot (x+2)}$

$\displaystyle =\lim_{x\to -2} \frac{\sqrt{x^2+5}+3}{x-2}$

Now plug in -2 again, so what's the limit?