Решите уравнение: 3/(x^2-6x+9)=1/(x+3 )-6/(9-x^2).

\[\frac{3}{x^{2} - 6x + 9} = \frac{1}{x + 3} - \frac{6}{9 - x^{2}}\]

\[\frac{3}{(x - 3)^{2}} = \frac{1}{x + 3} + \frac{6}{x^{2} - 9}\]

\[\frac{3}{(x - {3)}^{2}} = \frac{1^{\backslash x - 3}}{x + 3} + \frac{6}{(x - 3)(x + 3)}\]

\[\frac{3}{(x - 3)^{2}} = \frac{x - 3 + 6}{(x - 3)(x + 3)}\]

\[\frac{3}{(x - 3)^{2}} = \frac{1}{x - 3}\]

\[\frac{3}{(x - 3)^{2}} - \frac{1^{\backslash x - 3}}{x - 3} = 0\]

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

\[3 - x + 3 = 0\]

\[x = 6\]

\[Ответ:6.\]