Найдите корни уравнения: 1/(3x+1)-1/(9x^2+6x+1)=2.

\[\frac{1}{3x + 1} - \frac{1}{9x^{2} + 6x + 1} = 2\]

\[ОДЗ:\ \ x \neq - \frac{1}{3}\]

\[\frac{3x + 1 - 1}{9x^{2} + 6x + 1} = 2\]

\[3x = 2 \cdot \left( 9x^{2} + 6x + 1 \right)\]

\[3x = 18x^{2} + 12x + 2\]

\[18x^{2} + 12x + 2 - 3x = 0\]

\[18x^{2} + 9x + 2 = 0\]

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

\[= 81 - 4 \cdot 18 \cdot 2 =\]

\[= 81 - 144 < 0\ \]

\[Ответ:\ \ нет\ решений.\]