Решите уравнение методом замены переменной: (2x+1)/x+4x/3(2x+1)=-8/3.

\[\frac{2x + 1}{x} + \frac{4x}{3 \cdot (2x + 1)} = - \frac{8}{3}\ \]

\[Пусть\ \ t = \frac{2x + 1}{x};\ x \neq 0;\ \ \]

\[x \neq - \frac{1}{2}:\]

\[t + \frac{4}{3} \cdot \frac{1}{t} = - \frac{8}{3}\ \ \ | \cdot 3t\]

\[3t^{2} + 8t + 4 = 0\]

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

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

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