Verified answer

х ≠ 5

х ≠ - 5

[tex] \frac{x}{x + 5} + \frac{x + 5}{5 - x} = \frac{x - 45}{25 - {x}^{2} } \\ \frac{x}{x + 5} + \frac{x + 5}{5 - x} - \frac{x - 45}{(5 - x)(x + 5)} = 0 \\ \frac{x(5 - x) + (x + 5) {}^{2} - (x - 45) }{(5 - x)(x + 5)} = 0 \\ \frac{5x - {x}^{2} + {x}^{2} + 10x + 25 - x + 45}{(5 - x)(x + 5)} = 0 \\ \frac{14x + 70}{(5 - x)(x + 5)} = 0 \\ 14x + 70 = 0 \\ 14x = - 70 \\ x = - 70 \div 14 \\ x = - 5[/tex]

не подходит

Ответ: нет решений