\(\left(3b^3 + 3b^2 + 45b\right) \div 9b\)

\(\dfrac{b^2}{3} + \dfrac{b}{3} + 5\)

\(\left(4xy^2 - 2xy + 2x^2y\right) \div xy\)

\(4y - 2 + 2x\)

\(\left(3a^2b - 6ab + 5ab^2\right) \div ab\)

\(3a - 6 + 5b\)

\(\left(15q^6 + 5q^2\right)\left(5q^4\right)^{-1}\)

\(3q^2 + \dfrac{1}{q^2}\)

\(\left(4f^5 - 6f^4 + 12f^3 - 8f^2\right)\left(4f^2\right)^{-1}\)

\(f^3 - \dfrac{3}{2}f^2 + 3f - 2\)

\(\left(18x^4 - 12x^2 + 6x\right) \div 3x\)

\(6x^3 - 4x + 2\)

\(\left(3x^3 + 12x^2 - 9x\right) \div 3x\)

\(x^2 + 4x - 3\)

\(\left(12x^3y^2 - 15xy^4 + 20x^2\right) \div 4x^2y\)

$$\begin{align}
& \dfrac{12x^3y^2 - 15xy^4 + 20x^2}{4x^2y} \\[1em]
=\ & \dfrac{12x^3y^2}{4x^2y} - \dfrac{15xy^4}{4x^2y} + \dfrac{20x^2}{4x^2y} \\[1em]
=\ & 3xy - \dfrac{15y^3}{4x} + \dfrac{5}{y}
\end{align}$$