\(\dfrac{2x+6}{x^3-8}:\dfrac{\left(x+3\right)^3}{2x-4}=\dfrac{2\left(x+3\right)}{\left(x-2\right)\left(x^2+2x+4\right)}:\dfrac{\left(x+3\right)^3}{2\left(x-2\right)}\\ =\dfrac{2\left(x+3\right)}{\left(x-2\right)\left(x^2+2x+4\right)}.\dfrac{2\left(x-2\right)}{\left(x+3\right)^3}\\ =\dfrac{2.2}{\left(x^2+2x+\text{4}\right).\left(x+3\right)^2}=\dfrac{4}{\left(x+2x+4\right)\left(x+3\right)^2}\)
