Решите уравнение методом замены переменной: (x+4)/(x-2)+(x-2)/(x+4)=51/5.

\[\frac{x + 4}{x - 2} + \frac{x - 2}{x + 4} = 5\frac{1}{5}\]

\[Пусть\ \ t = \frac{x + 4}{x - 2};\ \ x \neq 2;\ \ \]

\[x \neq - 4:\]

\[t + \frac{1}{t} = \frac{26}{5}\ \ | \cdot 5t\]

\[5t^{2} - 26t + 5 = 0\]

\[D_{1} = 169 - 25 = 144\]

\[t_{1} = \frac{13 + 12}{5} = 5;\ \ \ \]

\[t_{2} = \frac{13 - 12}{5} = \frac{1}{5}.\]