Answer
$$0$$
Work Step by Step
We have
$$
\lim _{x \rightarrow \infty} \frac{x^{2/3}+3x}{x^{5/2}-x}=\frac{\infty}{\infty}.
$$
is an intermediate form, then we can apply L’Hôpital’s Rule as follows
$$
\lim _{x \rightarrow \infty} \frac{x^{2/3}+3x}{x^{5/2}-x}=\lim _{x \rightarrow \infty} \frac{(2/3)x^{-1/3}+3}{(5/2)x^{3/2}-1}=\frac{0+3}{\infty}=0.
$$
