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

Ответ:

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

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

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

\[4x^{2} - 9x + 2 = 0\]

\[x_{1} + x_{2} = \frac{9}{4}\]

\[x_{1} \cdot x_{2} = \frac{1}{2}\]

\[\Longrightarrow x_{1} = 2,\ \ x_{2} = \frac{1}{4}.\]

\[Ответ:x = 2;x = \frac{1}{4}.\]