\[\boxed{\mathbf{784\ (784).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{x^{2} - 9x - 10}{x^{2} - 1} = 0;\ \ \ \ \ \ x \neq 1;\ \ \ \ \]
\[x \neq - 1\]
\[x^{2} - 9x - 10 = 0\]
\[x_{1} + x_{2} = 9,\ \ x_{1}x_{2} = - 10,\ \]
\[\ x_{1} = 10,\ \ \]
\[x_{2} = - 1\ (не\ подходит)\]
\[Ответ:x = 10.\]
\[2)\ \frac{x^{2} + 5x - 14}{x^{2} - 6x + 8} = 0\]
\[x^{2} - 6x + 8 \neq 0\]
\[x_{1} + x_{2} = 6;\ \ \ \ \ \ x_{1} \cdot x_{2} = 8\]
\[x_{1} \neq 4;\ \ \ \ \ x_{2} \neq 2\]
\[x^{2} + 5x - 14 = 0\]
\[x_{1} + x_{2} = - 5;\ \ \ \ \ x_{1} \cdot x_{2} = - 14\]
\[x_{1} = - 7;\ \ \ \ \ \ \]
\[x_{2} = 2\ \ (не\ подходит)\]
\[Ответ:\ x = - 7.\]