Find the following limit or state that it does not exist.

$\underset{x2}{lim}\frac{x-2}{\sqrt[\phantom{2}]{2x21}-5}$

Simplify the given limit$.$

$\underset{x2}{lim}\frac{x-2}{\sqrt[\phantom{2}]{2x21}-5}=\underset{x2}{lim},($Simplify your answer.$)$

Evaluate the limit$,$ if possible. Select the correct choice below and, if necessary

A$.\underset{x2}{lim}\frac{x-2}{\sqrt[\phantom{2}]{2x21}-5}=,($Type an exact answer.$)$

B$.$ The limit does not exist.