Решите уравнение: (8c-3)/(4c^2-2c+1)+6/(8c^3+1)=2/(2c+1).

Ответ:

\[\frac{8c - 3}{4c^{2} - 2c + 1} + \frac{6}{8c^{3} + 1} = \frac{2}{2c + 1}\]

\[ОДЗ:\ \ 2c + 1 \neq 0\]

\[\ \ \ \ \ \ \ \ \Longrightarrow c \neq - 0,5\]

\[8c^{2} + 6c + 1 = 0\]

\[D = b^{2} - 4ac =\]

\[= 36 - 4 \cdot 8 \cdot 1 = 36 - 32 = 4\]

\[с_{1} = \frac{- 6 + 2}{16} = - \frac{4}{16} = - \frac{1}{4}\]

\[с_{2} = \frac{- 6 - 2}{16} = - \frac{8}{16} =\]

\[= - \frac{1}{2}\ (не\ подходит\ по\ ОДЗ)\]

\[Ответ:c = - \frac{1}{4}.\]