Для каких значении х верно равенство: (x^2-9x-52)/(x^2-17x+52)=(x+4)/(x-4).

\[x^{2} - 9x - 52 = 0\]

\[D = ( - 9)^{2} - 4 \cdot 1 \cdot ( - 52) =\]

\[= 81 + 208 = 289;\ \ \ \sqrt{D} = 17.\]

\[x_{1} = \frac{9 + 17}{2} = \frac{26}{2} = 13;\ \ \ \ \ \]

\[\text{\ \ \ }x_{2} = \frac{9 - 17}{2} = \frac{- 8}{2} = - 4\]

\[x^{2} - 17x + 52 = 0\]

\[D = ( - 17)^{2} - 4 \cdot 1 \cdot 52 =\]

\[= 289 - 208 = 81;\ \ \ \ \sqrt{D} = 9\]

\[x_{1} = \frac{17 - 9}{2} = \frac{8}{2} = 4;\ \ \ \ \ \ \]

\[\ x_{2} = \frac{17 + 9}{2} = \frac{26}{2} = 13\]

\[Ответ:для\ любых\ значений\ x.\]