Решите уравнение: (x-1)/x-3x/(2x-2)=-5/2.

\[\frac{x - 1}{x} - \frac{3x}{2x - 2} = - \frac{5}{2}\]

\[\frac{x - 1}{x} - \frac{3x}{2(x - 1)} = - \frac{5}{2}\ | \cdot 2x(x - 1)\]

\[ОДЗ:x \neq 1;\ \ x \neq 0.\]

\[2(x - 1)(x - 1) + 3x \cdot x = - 5x(x - 1)\]

\[2\left( x^{2} - 2x + 1 \right) + 3x^{2} = - 5x^{2} + 5x\]

\[2x^{2} - 4x + 2 + 8x^{2} - 5x = 0\]

\[10x^{2} - 9x + 2 = 0\]

\[D = 81 - 80 = 1\]

\[x_{1} = \frac{9 + 1}{20} = \frac{10}{20} = 0,5;\]

\[x_{2} = \frac{9 - 1}{20} = \frac{8}{20} = 0,4.\]

\[Ответ:x = 0,4;x = 0,5.\]