Решите уравнение методом замены переменной: 2/(x^2-5x+6)+3/(x^2-5x+7)=8/(x^2-5x+8).

\[\frac{2}{x^{2} - 5x + 6} + \frac{3}{x^{2} - 5x + 7} =\]

\[= \frac{8}{x^{2} - 5x + 8}\]

\[Пусть\ \ t = x^{2} - 5x + 6:\ \]

\[- 3t^{2} + 4t + 4 = 0\]

\[3t^{2} - 4t - 4 = 0\]

\[D_{1} = 4 + 12 = 16\]

\[t_{1} = \frac{2 + 4}{3} = 2;\ \ \ \]

\[t_{2} = \frac{2 - 4}{3} = - \frac{2}{3}.\]