\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}-\dfrac{2x^2+1}{4x^2-2x}\)
\(=\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}-\dfrac{2x^2+1}{2x\left(2x-1\right)}\)
\(=\dfrac{3\left(2x-1\right)}{2x\left(2x-1\right)}+\dfrac{2x\left(3x-3\right)}{2x\left(2x-1\right)}-\dfrac{2x^2+1}{2x\left(2x-1\right)}\)
\(=\dfrac{6x-3+6x^2-6x-2x^2-1}{2x\left(2x-1\right)}\)
\(=\dfrac{4x^2-4}{2x\left(2x-1\right)}\)
\(=\dfrac{4\left(x^1-1\right)}{2x\left(2x-1\right)}\)
\(=\dfrac{2\left(x^2-1\right)}{x\left(2x-1\right)}\)
\(=\dfrac{6x-3+6x^2-6x-2x^2-1}{2x\left(2x-1\right)}=\dfrac{4x^2-4}{2x\left(2x-1\right)}=\dfrac{4\left(x^2-1\right)}{2x\left(2x-1\right)}=\dfrac{2\left(x^2-1\right)}{x\left(2x-1\right)}\)
