Answer
$\lim\limits_{x \to 4}\frac{4-x}{5 - \sqrt (x^{2}+9)} = \frac{5}{4} = 1.25$
Work Step by Step
$\frac{4-x}{5 - \sqrt (x^{2}+9)} = \frac{(4-x)(5 + \sqrt (x^{2}+9))}{(5 - \sqrt (x^{2}+9))(5 + \sqrt (x^{2}+9))} = \frac{(4-x)(5 + \sqrt (x^{2}+9))}{25 - (x^{2}+9)} = = \frac{(4-x)(5 + \sqrt (x^{2}+9))}{(16-x^{2})} = \frac{(5 + \sqrt (x^{2}+9))}{(4+x)}$
Now,
$\lim\limits_{x \to 4}\frac{4-x}{5 - \sqrt (x^{2}+9)} = \lim\limits_{x \to 4}\frac{(5 + \sqrt (x^{2}+9))}{(4+x)} = \frac{(5+5)}{4+4} = \frac{10}{8} = \frac{5}{4} = 1.25$
