Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 25

$$\frac{1}{4}$$

\begin{align*} \lim _{x \rightarrow 4}\left(\frac{1}{\sqrt{x}-2}-\frac{4}{x-4}\right)&=\lim _{x \rightarrow 4} \frac{\sqrt{x}+2-4}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ &=\lim _{x \rightarrow 4} \frac{\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ &=\frac{1}{4} \end{align*}