1. **State the problem:** Simplify the expression $\frac{6x+9}{x}$. 2. **Recall the formula and rules:** When dividing a sum by a term, you can split the division over each term: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$ 3. **Apply the rule:** $$\frac{6x+9}{x} = \frac{6x}{x} + \frac{9}{x}$$ 4. **Simplify each term:** $$\frac{6x}{x} = \cancel{\frac{6\cancel{x}}{\cancel{x}}} = 6$$ 5. **Write the simplified expression:** $$6 + \frac{9}{x}$$ 6. **Final answer:** The simplified form of $\frac{6x+9}{x}$ is $$6 + \frac{9}{x}$$.