6)

\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)

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

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

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

\(=\dfrac{8x^2-2}{2x\left(2x-1\right)}\)

\(=\dfrac{2\left(4x^2-1\right)}{2x\left(2x-1\right)}\)

\(=\dfrac{2\left(2x+1\right)\left(2x-1\right)}{2\left(2x-1\right)}\)

\(=2x+1\)