Сократить дробь: (x^2+x-6)/(x^2-2x-15).

Ответ:

\[\frac{x^{2} + x - 6}{x^{2} - 2x - 15} = \frac{(x + 3)(x - 2)}{(x + 3)(x - 5)} =\]

\[= \frac{x - 2}{x - 5}.\]

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

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

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

\[2)\ x^{2} - 2x - 15 = (x + 3)(x - 5)\]

\[D_{1} = 1 + 15 = 16\]

\[x_{1} = 1 + 4 = 5;\]

\[x_{2} = 1 - 4 = - 3.\]