Splitting the Fraction

To divide a sum by a number, divide each term by that number. So $\frac{6x^{2}+9x}{3}$ splits into $\frac{6x^{2}}{3}+\frac{9x}{3}$. Now you have two small divisions instead of one large one.

In each piece, divide the coefficient: $\frac{6}{3} = 2$ and $\frac{9}{3} = 3$. The quotient is $2x^{2}+3x$. The powers of $x$ do not change, because the divisor 3 has no $x$ to cancel.

To check a division, multiply the quotient by the divisor. You should get the original sum back: $3\left(2x^{2}+3x\right) = 6x^{2}+9x$. Dividing a sum term by term is the distributive law used in reverse.