Решите уравнение: x^2-6x+7/(x-5)=7/(x-5)-5.

\[x² - 6x + \frac{7}{x - 5} = \frac{7}{x - 5} - 5\]

\[x^{2} - 6x + 5 = 0\]

\[D = ( - 6)^{2} - 4 \cdot 1 \cdot 5 =\]

\[= 36 - 20 = 16\]

\[x_{1} = \frac{6 + \sqrt{16}}{2} = \frac{6 + 4}{2} = \frac{10}{2} =\]

\[= 5\ (не\ подходит)\]

\[x_{2} = \frac{6 - \sqrt{16}}{2} = \frac{6 - 4}{2} = \frac{2}{2} = 1\]

\[Ответ:x = 1.\]