Для каких значении х верно равенство: (x^2-16x+55)/(x^2-6x-55)=(x-5)/(x+5).

\[x^{2} - 16x + 55 = 0\]

\[D = ( - 16)^{2} - 4 \cdot 1 \cdot 55 =\]

\[= 256 - 220 = 36;\ \ \ \ \sqrt{D} = 6.\]

\[x_{1} = \frac{16 + 6}{2} = \frac{22}{2} = 11;\ \ \ \ \ \]

\[\ x_{2} = \frac{16 - 6}{2} = \frac{10}{2} = 5\]

\[x^{2} - 6x - 55 = 0\]

\[D = ( - 6)^{2} - 4 \cdot 1 \cdot ( - 55) =\]

\[= 36 + 220 = 256;\ \ \ \ \sqrt{D} = 16.\]

\[x_{1} = \frac{6 + 16}{2} = \frac{22}{2} = 11;\ \ \]

\[\text{\ \ \ \ \ \ }x_{2} = \frac{6 - 16}{2} = \frac{- 10}{2} = - 5\]

\[Ответ:для\ любых\ значений\ \text{x.}\]