Answer
$$2$$
Work Step by Step
From the figure, we get:
$$\lim _{x \rightarrow 4} \frac{x-4}{\sqrt{x}-\sqrt{8-x}}=2$$
and algebraically, we get:
\begin{aligned}
\lim _{x \rightarrow 4} \frac{\sqrt{5-x}-1}{2-\sqrt{x}} &=\lim _{x \rightarrow 4} \frac{2+\sqrt{x}}{\sqrt{5-x}+1} \\
&=\frac{2+\sqrt{4}}{\sqrt{5-4}+1} \\
&=\frac{2+2}{\sqrt{1}+1}\\
&=2
\end{aligned}
