Answer
L’Hôpital’s Rule does not apply.
Work Step by Step
Since the denominator is non zero at $ x=3$, then L’Hôpital’s Rule does not apply. We can find the limit directly as follows
$$
\lim _{x \rightarrow 3} \frac{2 x^{2}-5 x-3}{x-4}=\frac{2 (9)-5 (3)-3}{3-4}=\frac{0}{-1}=0.
$$
