1. **State the problem:** Simplify or analyze the expression $$\frac{7x-4}{x+9}$$. 2. **Formula and rules:** This is a rational expression where the numerator is $7x-4$ and the denominator is $x+9$. Important rules: - The denominator cannot be zero, so $x \neq -9$. - Simplify by factoring if possible. 3. **Check for factoring:** - Numerator $7x-4$ cannot be factored further. - Denominator $x+9$ is already linear. 4. **Simplification:** Since no common factors exist, the expression is already in simplest form. 5. **Domain:** The expression is defined for all $x$ except $x = -9$. **Final answer:** The expression $$\frac{7x-4}{x+9}$$ is simplified and defined for all $x \neq -9$.