## Task B-1.2.

Solve the inequality $\left(1-\frac{4 x^{3}-x}{x-2 x^{2}}\right)^{-3}>0$.
## First solution.

Notice that the numerator and denominator of the fraction in parentheses can be factored and simplified, so we get

$$
\left(1+\frac{x(2 x-1)(2 x+1)}{x(2 x-1)}\right)^{-3}>0
$$

and from there, under the condition $x \neq 0, x \neq \frac{1}{2}$

$(2 x+2)^{-3}>0$ or $\frac{1}{(2 x+2)^{3}}>0$.

It follows that $2 x+2>0$, or $x>-1$, so

$$
x \in\langle-1,+\infty\rangle \backslash\left\{0, \frac{1}{2}\right\}
$$