Сократите дробь: (a^2-16a+63)/(a^2-81).

Ответ:

\[\frac{a^{2} - 16a + 63}{a^{2} - 81} =\]

\[= \frac{(a - 7)(a - 9)}{(a - 9)(a + 9)} = \frac{a - 7}{a + 9}\]

\[a^{2} - 16a + 63 = (a - 7)(a - 9)\]

\[D = 64 - 63 = 1\]

\[a_{1} = 8 - 1 = 7;\ \ \ a_{2} = 8 + 1 = 9.\]