a) \(\dfrac{4x^2-9y^2}{2x-3y}=\dfrac{\left(2x-3y\right)\left(2x+3y\right)}{2x-3y}=2x+3y\)

b)\(\dfrac{27x^3-1}{3x-1}=\dfrac{\left(3x-1\right)\left(9x^2+3x+1\right)}{3x-1}=9x^2+3x+1\)

c) \(\dfrac{8x^3+1}{4x^2-2x+1}=\dfrac{\left(2x+1\right)\left(4x^2-2x+1\right)}{4x^2-2x+1}=2x+1\)

d)\(\dfrac{x^2-3x+xy-3y}{x+y}=\dfrac{\left(x+y\right)\left(x-3\right)}{x+y}=x-3\)