\(a,=\dfrac{1-2x+3+2y+2x-4}{6x^3y}=\dfrac{2y}{6x^3y}=\dfrac{1}{3x^2}\\ b,=\dfrac{4x-8+2x+4-5x+6}{\left(x+2\right)\left(x-2\right)}=\dfrac{x-2}{\left(x-2\right)\left(x+2\right)}=\dfrac{1}{x+2}\\ c,=\dfrac{x^2+2+2x-2-x^2-x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{1}{x^2+x+1}\\ d,=\dfrac{1}{\left(x+3\right)^2}-\dfrac{1}{\left(x-3\right)^2}+\dfrac{x}{\left(x-3\right)\left(x+3\right)}\\ =\dfrac{x^2-6x+9-x^2-6x-9+x^3-9x}{\left(x+3\right)^2\left(x-3\right)^2}=\dfrac{x^3-21x}{\left(x+3\right)^2\left(x-3\right)^2}\)