a) \(14x^3y:10x^2=\dfrac{7}{5}xy\)
b) \(\left(x^3-27\right):\left(3-x\right)\)
\(=\left(x-3\right)\left(x^2+3x+9\right):\left(3-x\right)\)
\(=-\left(3-x\right)\left(x^2+3x+9\right):\left(3-x\right)\)
\(=-\left(x^2+3x+9\right)\)
\(=-x^2-3x-9\)
c) \(8x^3y^3z:6xy^3=\dfrac{4}{3}x^2z\)
d) \(\left(x^2-9y^2+4x+4\right):\left(x^2+3y+2\right)\)
\(=\left[\left(x+2\right)^2-\left(3y\right)^2\right]:\left(x^2+3y+2\right)\)
\(=\left(x+3y+2\right)\left(x-3y+2\right):\left(x^2+3y+2\right)\)
\(=x-3y+2\)