For what value $k$ is $f(x) = \begin{cases} \frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2} & x \neq 2 \\ k & x = 2 \end{cases}$ continuous at $x=2$? For what value $k$ is the following function continuous at $x=2$?
$$f(x) = \begin{cases}
\frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2} & x \neq 2 \\
k & x = 2
\end{cases}$$

All those square roots are weighing me down!  And $k$?  My mind's not where it's supposed to be today.  Thanks in advance for posting a solution!

Hint :
$$\frac{\sqrt{2x+5}-\sqrt{x+7}}{x-2}=\frac1{\sqrt{2x+5}+\sqrt{x+7}}\xrightarrow[x\to2]{} ...$$
