a: \(=\dfrac{12x+3-6x-4}{6}=\dfrac{6x-1}{6}\)
b: \(=\dfrac{x^2-9-x^2+9}{x\left(x-3\right)}=0\)
c: \(=\dfrac{x\left(x+3\right)-x+1}{x\left(x+1\right)\left(x-1\right)}=\dfrac{x^2+2x+1}{x\left(x+1\right)\left(x-1\right)}=\dfrac{x+1}{x\left(x-1\right)}\)
d: \(=\dfrac{3x+2-12x+8+10x-8}{\left(3x+2\right)\left(3x-2\right)}=\dfrac{x+2}{\left(3x+2\right)\left(3x-2\right)}\)
e: \(=\dfrac{3}{2x\left(x+1\right)}+\dfrac{2x-1}{\left(x+1\right)\left(x-1\right)}-\dfrac{2}{x}\)
\(=\dfrac{3x-3+2x\left(2x-1\right)-2\cdot2\left(x^2-1\right)}{2x\left(x+1\right)\left(x-1\right)}\)
\(=\dfrac{3x-3-4x^2+4+4x^2-2x}{2x\left(x+1\right)\left(x-1\right)}=\dfrac{x+1}{2x\left(x+1\right)\left(x-1\right)}=\dfrac{1}{2x\left(x-1\right)}\)
