Решение:

$$rac{3}{x-3} - rac{x+15}{x^2-9} - rac{2}{x} = rac{3}{x-3} - rac{x+15}{(x-3)(x+3)} - rac{2}{x}$$

$$rac{3x(x+3) - x(x+15) - 2(x-3)(x+3)}{x(x-3)(x+3)} = rac{3x^2 + 9x - x^2 - 15x - 2(x^2-9)}{x(x-3)(x+3)}$$

$$rac{3x^2 + 9x - x^2 - 15x - 2x^2 + 18}{x(x-3)(x+3)} = rac{(3x^2 - x^2 - 2x^2) + (9x - 15x) + 18}{x(x-3)(x+3)}$$

$$rac{0 - 6x + 18}{x(x-3)(x+3)} = rac{-6x + 18}{x(x-3)(x+3)} = rac{-6(x-3)}{x(x-3)(x+3)} = rac{-6}{x(x+3)}$$

Ответ: $$ \frac{-6}{x(x+3)} $$