Verified answer

[tex]\frac{x+5}{x^{2} - 5x}[/tex] - [tex]\frac{x+25}{2x^{2} -50}[/tex] = [tex]\frac{x-5}{2x^{2} +10x}[/tex]

[tex]\frac{x+5}{x(x-5)}[/tex] - [tex]\frac{x+25}{2(x+5)(x-5)}[/tex] = [tex]\frac{x-5}{2x(x+5)}[/tex]

[tex]\frac{x+5}{x(x-5)}[/tex] - [tex]\frac{x+25}{2(x+5)(x-5)}[/tex] - [tex]\frac{x-5}{2x(x+5)}[/tex] = 0

[tex]\frac{2(x+5)(x+5)}{2x(x-5)(x+5)}[/tex] - [tex]\frac{x(x+25)}{2x(x-5)(x+5)}[/tex] - [tex]\frac{(x-5)(x-5)}{2x(x-5)(x+5)}[/tex] = 0

[tex]\frac{2(x+5)(x+5) - x(x+25) - (x-5)(x-5)}{2x(x-5)(x+5)}[/tex] = 0

2x(x-5)(x+5) ≠ 0

x ≠ 0, x ≠ 5, x ≠ -5

2(x+5)(x+5) - x(x+25) - (x-5)(x-5) = 0

2x² + 10x + 10x + 50 - x² - 25x - x² + 5x + 5x - 25 = 0

5x - 25 = 0

5(x-5) = 0

x = 5

Ответ: Нет решений