4. Упростите выражение $$rac{5}{x-7} - \frac{2}{x} - \frac{3x}{x^2-49} + \frac{21}{49-x^2}$$.

$$\frac{5}{x-7} - \frac{2}{x} - \frac{3x}{x^2-49} + \frac{21}{49-x^2} = \frac{5}{x-7} - \frac{2}{x} - \frac{3x}{(x-7)(x+7)} - \frac{21}{x^2-49} = \frac{5}{x-7} - \frac{2}{x} - \frac{3x}{(x-7)(x+7)} - \frac{21}{(x-7)(x+7)} = \frac{5x(x+7) - 2(x-7)(x+7) - 3x(x) - 21x}{x(x-7)(x+7)} = \frac{5x^2 + 35x - 2(x^2 - 49) - 3x^2 - 21x}{x(x-7)(x+7)} = \frac{5x^2 + 35x - 2x^2 + 98 - 3x^2 - 21x}{x(x-7)(x+7)} = \frac{(5x^2 - 2x^2 - 3x^2) + (35x - 21x) + 98}{x(x-7)(x+7)} = \frac{14x + 98}{x(x-7)(x+7)} = \frac{14(x+7)}{x(x-7)(x+7)} = \frac{14}{x(x-7)}$$ Ответ: $$\frac{14}{x(x-7)}$$