Question

How do I simplify this?

Answer 1

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