\(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)\(\left(ĐKXĐ:x\ne\pm\dfrac{1}{3}\right)\)
\(=\left[\dfrac{-3x\left(3x+1\right)+2x\left(3x-1\right)}{\left(3x-1\right)\left(3x+1\right)}\right]:\dfrac{2x\left(3x+5\right)}{\left(3x-1\right)^2}\)
\(=\dfrac{-9x^2-3x+6x^2-2x}{\left(3x-1\right)\left(3x+1\right)}.\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{-3x^2-5x}{\left(3x-1\right)\left(3x+1\right)}.\dfrac{\left(3x-1\right)^2}{2x\left(3x+5\right)}\)
\(=\dfrac{-x\left(3x+5\right).\left(3x-1\right)^2}{\left(3x-1\right)\left(3x+1\right).2x\left(3x+5\right)}\)
\(=\dfrac{1-3x}{2\left(3x+1\right)}\)
\(=\dfrac{1-3x}{6x+2}\)
