Решение:

a) $$\frac{3x-1}{x^2} + \frac{x-9}{3x} = \frac{3(3x-1)+x(x-9)}{3x^2} = \frac{9x-3+x^2-9x}{3x^2} = \frac{x^2-3}{3x^2}$$ Ответ: $$\frac{x^2-3}{3x^2}$$

б) $$\frac{1}{2a-b} - \frac{1}{2a+b} = \frac{2a+b-(2a-b)}{(2a-b)(2a+b)} = \frac{2a+b-2a+b}{4a^2-b^2} = \frac{2b}{4a^2-b^2}$$ Ответ: $$\frac{2b}{4a^2-b^2}$$

в) $$\frac{5}{c+3} - \frac{5c-2}{c^2+3c} = \frac{5}{c+3} - \frac{5c-2}{c(c+3)} = \frac{5c-(5c-2)}{c(c+3)} = \frac{5c-5c+2}{c(c+3)} = \frac{2}{c(c+3)}$$ Ответ: $$\frac{2}{c(c+3)}$$