How can I determine limit: $\lim\limits_{x\to4}\frac{x-4}{x-\sqrt[]{x}-2}$? How can I determine limit:
$$\lim_{x\to4}\frac{x-4}{x-\sqrt[]{x}-2}$$
Thanks

If you are unfamiliar with L'Hopital's rule, this is what you can do.
$$ \lim_{x \rightarrow 4} \frac{ x - 4 } { x - \sqrt{x} - 2} = \lim_{x \rightarrow 4} \frac{ (\sqrt{x} - 2) ( \sqrt{x} + 2) } { (\sqrt{x} -2) ( \sqrt{x} +1) }=  \lim_{x \rightarrow 4} \frac{ ( \sqrt{x} + 2) } { ( \sqrt{x} +1) } = \frac{ 4}{3}.$$
