Решите неравенство: x^2/(x-3)>-9/(3-x).

Ответ:

\[\frac{x^{2}}{x - 3} > - \frac{9}{3 - x}\]

\[\frac{x^{2}}{x - 3} > \frac{9}{x - 3}\]

\[\frac{x^{2} - 9}{x - 3} > 0\]

\[\frac{(x + 3)(x - 3)}{x - 3} > 0;\ \ x \neq 3\]

\[x + 3 > 0\]

\[x > - 3.\]

\[- 3 < x < 3;\ \ x > 3.\]