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