15 Найдите значение выражения \(\frac{x^2+10x+25}{3x^2-75} - \frac{x^2}{3x^2-15x}\) при \(x = 4\frac{1}{6}\)

Преобразуем выражение: \(\frac{x^2+10x+25}{3x^2-75} - \frac{x^2}{3x^2-15x} = \frac{(x+5)^2}{3(x^2-25)} - \frac{x^2}{3x(x-5)} = \frac{(x+5)^2}{3(x-5)(x+5)} - \frac{x^2}{3x(x-5)} = \frac{x+5}{3(x-5)} - \frac{x}{3(x-5)} = \frac{x+5-x}{3(x-5)} = \frac{5}{3(x-5)}\) Подставим \(x = 4\frac{1}{6} = \frac{25}{6}\) \(\frac{5}{3(\frac{25}{6}-5)} = \frac{5}{3(\frac{25-30}{6})} = \frac{5}{3(-\frac{5}{6})} = \frac{5}{-\frac{15}{6}} = 5 \cdot (-\frac{6}{15}) = -\frac{30}{15} = -2\) Ответ: -2