Answer
$\lim\limits_{x \to -3}\frac{2 - \sqrt {x^{2}-5}}{x+3} = \frac{3}{2} = 1.5$
Work Step by Step
$\frac{2 - \sqrt (x^{2}-5)}{x+3} = \frac{(2 - \sqrt (x^{2}-5))(2 + \sqrt (x^{2}-5))}{(x+3)(2 + \sqrt (x^{2}-5))} = \frac{4-(x^{2}-5)}{(x+3)(2 + \sqrt (x^{2}-5))} = \frac{-(x^{2} - 9)}{(x+3)(2 + \sqrt (x^{2}-5))}$
= $\frac{-(x+3)(x-3)}{(x+3)(2 + \sqrt (x^{2}-5))}$
= $\frac{-(x-3)}{(2 + \sqrt (x^{2}-5))}$
Now,
$\lim\limits_{x \to -3}\frac{2 - \sqrt (x^{2}-5)}{x+3} = \lim\limits_{x \to -3}\frac{-(x-3)}{(2 + \sqrt (x^{2}-5))} = \frac{-(-3-3)}{2+2} = \frac{6}{4} = 1.5$
