Представьте в виде дроби: a) $$rac{3x-1}{x^2} + \frac{x-9}{3x}$$; б) $$rac{5}{c+3} - \frac{5c-2}{c^2+3c}$$; в) $$\frac{3x^2-8y^2}{x^2-2xy} - \frac{3xy-x^2}{xy-2y^2}$$

a) $$\frac{3x-1}{x^2} + \frac{x-9}{3x} = \frac{3(3x-1) + x(x-9)}{3x^2} = \frac{9x-3 + x^2 - 9x}{3x^2} = \frac{x^2-3}{3x^2}$$ б) $$\frac{5}{c+3} - \frac{5c-2}{c^2+3c} = \frac{5}{c+3} - \frac{5c-2}{c(c+3)} = \frac{5c - (5c-2)}{c(c+3)} = \frac{5c - 5c + 2}{c(c+3)} = \frac{2}{c(c+3)}$$ в) $$\frac{3x^2-8y^2}{x^2-2xy} - \frac{3xy-x^2}{xy-2y^2} = \frac{3x^2-8y^2}{x(x-2y)} - \frac{3xy-x^2}{y(x-2y)} = \frac{y(3x^2-8y^2) - x(3xy-x^2)}{xy(x-2y)} = \frac{3x^2y - 8y^3 - 3x^2y + x^3}{xy(x-2y)} = \frac{x^3 - 8y^3}{xy(x-2y)} = \frac{(x-2y)(x^2 + 2xy + 4y^2)}{xy(x-2y)} = \frac{x^2 + 2xy + 4y^2}{xy}$$