Решите уравнение методом замены переменной: (5x-1)/(x-2)+5(x-2)/(5x+1)=6.

\[\frac{5x - 1}{x - 2} + \frac{5 \cdot (x - 2)}{5x - 1} = 6\]

\[Пусть\ \ t = \frac{5x - 1}{x - 2};\ \ x \neq 2;\ \]

\[x \neq \frac{1}{5}:\ \]

\[t + 5 \cdot \frac{1}{t} = 6\ \ \ \ \ \ | \cdot t\]

\[t² - 6t + 5 = 0\]

\[t_{1} + t_{2} = 6;\ \ \ t_{1} \cdot t_{2} = 5\]

\[t_{1} = 5,\ \ t_{2} = 1.\]