Determine the following limit$,$ using $$ or $-$ when appropriate, or state that it does not exist.

$\underset{x{3}^{}}{lim}\frac{x-4}{\sqrt[\phantom{2}]{x-3}}$

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\underset{x{3}^{}}{lim}\frac{x-4}{\sqrt[\phantom{2}]{x-3}}=($Simplify your answer.$)$

B$.$ The limit does not exist and is neither $$ nor $-.$