[tex]\bf \cfrac{x^3+6x^2+3x+18}{3x^2+9}\div \cfrac{x+6}{x+1}\\\\
-----------------------------\\\\
(x^3+6x^2)+(3x+18)\implies x^2\underline{(x+6)}+3\underline{(x+6)}\leftarrow \textit{common \underline{factor}}
\\\\\\
(x+6)(x^2+3)\\\\
-----------------------------\\\\
thus\\\\\\
\cfrac{(x+6)(x^2+3)}{3(x^2+3)}\div \cfrac{x+6}{x+1}\implies \cfrac{(x+6)(x^2+3)}{3(x^2+3)}\cdot \cfrac{x+1}{x+6}
\\\\\\
\cfrac{x+1}{3}[/tex]
