\( \lim \limits_{x \rightarrow 3}\left(\frac{1}{x-3}-\frac{4}{x^{1}-2 x-3}\right) \)
\( =\lim \limits_{x \rightarrow 3}\left(\frac{1}{x-3}-\frac{4}{(x+1)(x-3)}\right) \)
\( =\lim \limits_{x \rightarrow 3}\left(\frac{x+1-4}{(x+1)(x-3)}\right) \)
\( =\lim \limits_{x \rightarrow 3}\left(\frac{x-3}{(x+1)(x-3)}\right) . \)
\( =\lim \limits_{x \rightarrow 3}\left(\frac{1}{x+1}\right)=\frac{1}{4} \)