Найдите решения уравнения (3x+2)/(2x+3)+(2x+3)/(3x+2)+2=0.

Ответ:

\[\frac{3x + 2^{\backslash 3x + 2}}{2x + 3} + \frac{2x + 3^{\backslash 2x + 3}}{3x + 2} + 2^{\backslash(2x + 3)(3x + 2)} = 0\]

\[ОДЗ:\ \ x \neq - 1,5;\ \ x \neq - \frac{2}{3}\]

\[9x^{2} + 12x + 4 + 4x^{2} + 12x + 9 +\]

\[+ 2 \cdot \left( 6x^{2} + 9x + 4x + 6 \right) = 0\]

\[13x^{2} + 24x + 13 + 12x^{2} + 26x + 12 = 0\]

\[25x^{2} + 50x + 25 = 0\ \ \ \ |\ :25\]

\[x^{2} + 2x + 1 = 0\]

\[(x + 1)^{2} = 0\]

\[x + 1 = 0\]

\[x = - 1.\]

\[Ответ:x = - 1.\]