1. **State the problem:** Divide the expression $12g^2 + 18$ by $2g$ and express the result including any remainder as a simplified fraction. 2. **Write the division as a fraction:** $$\frac{12g^2 + 18}{2g}$$ 3. **Split the fraction into two parts:** $$\frac{12g^2}{2g} + \frac{18}{2g}$$ 4. **Simplify each term:** - For the first term: $$\frac{12g^2}{2g} = \frac{\cancel{12}^6 \cancel{g^2}^{g}}{\cancel{2}^1 \cancel{g}^1} = 6g$$ - For the second term: $$\frac{18}{2g} = \frac{\cancel{18}^9}{\cancel{2}^1 g} = \frac{9}{g}$$ 5. **Combine the simplified terms:** $$6g + \frac{9}{g}$$ 6. **Interpretation:** The division results in $6g$ plus a remainder expressed as the fraction $\frac{9}{g}$. **Final answer:** $$6g + \frac{9}{g}$$