Сократите дробь: (y^2-8y+12)/(12y-y^2-20).

Ответ:

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

\[y_{1} + y_{2} = 8\]

\[y_{1} \cdot y_{2} = 12\]

\[\Longrightarrow y_{1} = 6;\ \ y_{2} = 2.\]

\[y^{2} - 8y + 12 = (y - 6)(y - 2).\]

\[12y - y^{2} - 20 = 0\]

\[y^{2} - 12y + 20 = 0\]

\[y_{1} + y_{2} = 12\]

\[y_{1} \cdot y_{2} = 20\]

\[\Longrightarrow y_{1} = 10;\ \ y_{2} = 2\]

\[12y - y^{2} - 20 =\]

\[= - (y - 10)(y - 2) =\]

\[= (10 - y)(y - 2).\]