2. Solve the equation

$$
\frac{x \sqrt[3]{x}-1}{\sqrt[3]{x^{2}}-1}-\frac{\sqrt[3]{x^{2}}-1}{\sqrt[3]{x}+1}=4
$$
Solution. We introduce the substitution $t=\sqrt[3]{x}$, which transforms the equation into:

$$
\frac{t^{4}-1}{t^{2}-1}-\frac{t^{2}-1}{t-1}=4
$$

For $t \neq -1$ and $t \neq 1$, this equation is equivalent to the equation

$$
t^{2}+1-t+1=4
$$

i.e.

$$
t^{2}-t-2=0
$$

whose solutions are: $t_{1}=-1$ and $t_{2}=2$. Since $t \neq -1$, the only solution to the equation is $x$ for which $\sqrt[3]{x}=2$, i.e., $x=8$.