Решите неравенство: x^4+3x^3<=(81x+243)/x.

\[x^{4} + 3{x^{3}}^{\backslash x} \leq \frac{81x + 243}{x}\]

\[\frac{\left( x^{4} + 3x^{3} \right)x - (81x + 243)}{x} \leq 0\]

\[\frac{x^{4}(x + 3) - 81 \cdot (x + 3)}{x} \leq 0\]

\[\frac{(x + 3)(x^{4} - 81)}{x} \leq 0\]

\[\frac{(x + 3)(x^{2} - 9)(x^{2} + 9)}{x} \leq 0\]

\[\frac{(x + 3)(x - 3)(x + 3)}{x} \leq 0\]

\[\frac{(x + 3)^{2}(x - 3)}{x} \leq 0\]

\[Ответ:\ \left\{ - 3 \right\} \cup (0;3\rbrack.\]