Сократите дробь: (x^2+5x-24)/(4x-x^2-3).

Ответ:

\[x_{1} + x_{2} = - 5;\ \ x_{1} \cdot x_{2} = - 24\]

\[x_{1} = - 8;\ \ x_{2} = 3\]

\[x^{2} + 5x - 24 = (x + 8)(x - 3).\]

\[x^{2} - 4x + 3 = 0\]

\[x_{1} + x_{2} = 4;\ \ x_{1} \cdot x_{2} = 3\]

\[x_{1} = 3;\ \ x_{2} = 1\]

\[- x^{2} + 4x - 3 =\]

\[= - (x - 3)(x - 1) =\]

\[= (x - 3)(1 - x).\]