calculus - Can I not use L'hopital rule here?

The question is:

$$
\lim_{x\to-\infty}\frac{\sqrt{16x^2+3}}{5x-2}
$$

The given solution is:

This makes sense since as $x$ approaches negative infinity, we look at the left side of the $\sqrt{x^2}$ function, which is $-x$.

I tried using L'hopital rule before looking at the answer and got that the limit was $0$. Am I not allowed to use L'hopital here? I think I am. As $x$ approaches negative infinity, the numerator approaches infinity, and the denominator approaches negative infinity. We want to see which approaches their limit faster, so we look at their rates of change, i.e. their derivatives. So I fugured we could use L'hopital here.

Am I misunderstanding something?

Thanks