Сократить дробь: (x^2-x-6)/(x^2-3x-10).

Ответ:

\[\frac{x^{2} - x - 6}{x^{2} - 3x - 10} =\]

\[= \frac{(x + 2)(x - 3)}{(x + 2)(x - 5)} = \frac{x - 3}{x - 5}.\]

\[1)\ x^{2} - x - 6 = (x + 2)(x - 3)\]

\[x_{1} + x_{2} = 1;x_{1} \cdot x_{2} = - 6\]

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

\[2)\ x^{2} - 3x - 10 = (x + 2)(x - 5)\]

\[x_{1} + x_{2} = 3;\ \ x_{1} \cdot x_{2} = - 10\]

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