a: \(A=\dfrac{2x^3-4x^2}{3x^2-6x}=\dfrac{2x^2\left(x-2\right)}{3x\left(x-2\right)}=\dfrac{2x}{3}\)
b: \(B=\dfrac{x^2-xy+x-y}{x^2+xy+x+y}\)
\(=\dfrac{x\left(x-y\right)+\left(x-y\right)}{x\left(x+y\right)+\left(x+y\right)}\)
\(=\dfrac{\left(x-y\right)\left(x+1\right)}{\left(x+y\right)\left(x+1\right)}=\dfrac{x-y}{x+y}\)
c: \(C=\dfrac{2a+2b-2}{\left(a-1\right)^2-b^2}\)
\(=\dfrac{2\left(a+b-1\right)}{\left(a-1-b\right)\left(a-1+b\right)}\)
\(=\dfrac{2}{a-1-b}\)
d: \(D=\dfrac{x^2-2x+1}{\left(x-1\right)\left(x+3\right)+x^2-1}\)
\(=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+3\right)+\left(x-1\right)\left(x+1\right)}\)
\(=\dfrac{\left(x-1\right)^2}{\left(x-1\right)\left(x+3+x+1\right)}\)
\(=\dfrac{x-1}{2x+4}\)
d: \(E=\dfrac{x^2-5x+4}{x^2+x-2}\)
\(=\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x+2\right)\left(x-1\right)}\)
\(=\dfrac{x-4}{x+2}\)