Решите уравнение: y^2/(y^2-6y)=(4(3-2y))/(y(6-y).

\[\frac{y^{2}}{y^{2} - 6y} = \frac{4(3 - 2y)}{y(6 - y)}\]

\[\frac{y^{2}}{y(y - 6)} = - \frac{4(3 - 2y)}{y(y - 6)}\]

\[ОДЗ:y(y - 6) \neq 0\]

\[y \neq 0;\ \ y \neq 6.\]

\[y^{2} = - 4(3 - 2y)\]

\[y^{2} = - 12 + 8y\]

\[y^{2} - 8y + 12 = 0\]

\[D_{1} = 16 - 12 = 4\]

\[y_{1} = 4 - 2 = 2;\]

\[y_{2} = 4 + 2 = 6\ (не\ подходит).\]

\[Ответ:y = 2.\]