\(K=\left(\dfrac{x+2}{3x}+\dfrac{2}{x+1}-3\right):\dfrac{2-4x}{x+1}-\dfrac{3x+1-x^2}{3x}\)\(=\left(\dfrac{\left(x+1\right)\left(x+2\right)}{3x\left(x+1\right)}+\dfrac{2.3x}{3x\left(x+1\right)}-\dfrac{3.3x\left(x+1\right)}{3x\left(x+1\right)}\right).\dfrac{x+1}{2\left(1-2x\right)}-1+\dfrac{1}{3x}-\dfrac{x}{3}\)\(=\dfrac{x^2+3x+2+6x-9x^2-9x}{3x\left(x+1\right)}.\dfrac{x+1}{2\left(1-2x\right)}+\dfrac{1}{3x}-\dfrac{x}{3}-1\)\(=\dfrac{-2\left(4x^2-1\right)}{3x}.\dfrac{1}{-2\left(2x-1\right)}+\dfrac{1+x^2}{3x}-1\)
\(=\dfrac{-2\left(2x-1\right)\left(2x+1\right)}{3x}.\dfrac{1}{-2\left(2x-1\right)}+\dfrac{1+x^2}{3x}-1\)\(=\dfrac{2x+1}{3x}+\dfrac{1+x^2}{3x}-1\)
\(=\dfrac{\left(x+1\right)^2}{3x}-1\)
