Решить уравнение: 4/(x^2-9)-(x+1)/(x-3)=1.

\[\frac{4}{x^{2} - 9} - \frac{x + 1^{\backslash x + 3}}{x - 3} = 1^{\backslash x^{2} - 9}\]

\[ОДЗ:x \neq \pm 3.\]

\[4 - x^{2} - x - 3x - 3 = x^{2} - 9\]

\[2x^{2} + 4x - 10 = 0\ \ \ |\ :2\]

\[x^{2} + 2x - 5 = 0\]

\[D_{1} = 1 + 5 = 6\]

\[x_{1,2} = - 1 \pm \sqrt{6}.\]

\[Ответ:x = - 1 \pm \sqrt{6}.\]