\(\dfrac{2x+6}{3x^2-x}:\dfrac{x^2+3x}{1-3x}\)
\(=\dfrac{2x+6}{3x^2-x}.\dfrac{1-3x}{x^2+3x}\)
\(=\dfrac{2\left(x+3\right)}{x\left(3x-1\right)}.\dfrac{1-3x}{x\left(x+3\right)}\)
\(=-\dfrac{2\left(x+3\right)\left(3x-1\right)}{x^2\left(3x-1\right)\left(x+3\right)}\)
\(=-\dfrac{2}{x^2}.\)