Решите уравнение методом замены переменной: (4x-3)/(x+1)+4(x+1)/(4x-3)=5.

\[\frac{4x - 3}{x + 1} + \frac{4 \cdot (x + 1)}{4x - 3} = 5\]

\[Пусть\ \ t = \frac{4x - 3}{x + 1};\ \ x \neq \frac{3}{4};\ \ \]

\[x \neq - 1:\]

\[t + 4\frac{1}{t} = 5\ \ \ \ \ \ \ \ | \cdot t\]

\[t² - 5t + 4 = 0\]

\[t_{1} + t_{2} = 5;\ \ t_{1} \cdot t_{2} = 4\]

\[t_{1} = 4,\ \ t_{2} = 1.\]