$\displaystyle \lim_{x \to -3} \frac{\sqrt{2x+22}\,-4}{x+3}\; (\frac{0}{0}\,form)$
$\text{Using L'Hôpital's rule}$
$\displaystyle \lim_{x \to -3} \frac{\frac{1}{2\sqrt{2x+22}}(2)\,-0}{1+0} =\lim_{x \to -3}\frac{1}{\sqrt{2x+22}} =\frac{1}{\sqrt{2(-3)+22}} =\frac{1}{4}=0.25$