Сократите дробь: (y^3+7y^2-60y)/(10y-50).

Ответ:

\[\frac{y^{3} + 7y^{2} - 60y}{10y - 50} =\]

\[= \frac{y\left( y^{2} + 7y - 60 \right)}{10 \cdot (y - 5)} =\]

\[= \frac{y(y - 5)(y + 12)}{10(y - 5)} = \frac{y^{2} + 12y}{10}\]

\[y^{2} + 7y - 60 = (y - 5)(y + 12)\]

\[y_{1} + y_{2} = - 7;\ \ y_{1} \cdot y_{2} = - 60\]

\[y_{1} = 5;\ \ y_{2} = - 12.\]