Решите систему неравенств: x^2/(x-3)<0; 36-x^2>=0.

Ответ:

\[\left\{ \begin{matrix} \frac{x^{2}}{x - 3} < 0\ \ \ \ \\ 36 - x^{2} \geq 0 \\ \end{matrix} \right.\ \]

\[x \neq 0;\]

\[\left\{ \begin{matrix} x - 3 < 0\ \ \ \ \ \\ x^{2} - 36 \leq 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x < 3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ (x + 6)(x - 6) \leq 0 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x < 3\ \ \ \ \ \ \ \ \ \ \ \\ - 6 \leq x \leq 6 \\ \end{matrix} \right.\ \]

\[- 6 \leq x < 0;\]

\[0 < x < 3.\]

\[Ответ:\ - 6 \leq x < 0;0 < x < 3.\]