\[\boxed{\text{59}\text{\ (59)}\text{.\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[1)\ \frac{x^{2} - 16}{x + 4} = - 8;\ \ \ x \neq - 4\]
\[\frac{(x - 4)(x + 4)}{(x + 4)} = - 8\]
\[x - 4 = - 8\]
\[x = - 8 + 4\]
\[x = - 4\]
\[Ответ:корней\ нет.\]
\[2)\ \frac{|x| - 7}{x - 7} = 0;\ \ \ \ \ x \neq 7\]
\[\frac{x - 7}{x - 7} = 0\]
\[1 \neq 0\]
\[Решений\ нет.\]
\[\frac{- x - 7}{x - 7} = 0\]
\[- x = 7\]
\[x = - 7\]
\[Ответ:\ x = - 7.\]