Решите неравенство: (x^2+15x+56)/(x^2-12x+20)<0.

Ответ:

\[\frac{x^{2} + 15x + 56}{x^{2} - 12x + 20} < 0\]

\[1)\ x^{2} + 15x + 56 =\]

\[= (x + 8)(x + 7)\]

\[x_{1} + x_{2} = - 15;\ \ \ x_{1} \cdot x_{2} = 56\]

\[x_{1} = - 7;\ \ \ x_{2} = - 8.\]

\[2)\ x^{2} - 12x + 20 =\]

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

\[x_{1} + x_{2} = 12;\ \ x_{1} \cdot x_{2} = 20\]

\[x_{1} = 10;\ \ \ x - 2 = 2.\]

\[\frac{(x + 8)(x + 7)}{(x - 2)(x - 10)} < 0\]

\[- 8 < x < - 7;\ \ 2 < x < 10.\]