1. **State the problem:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and rules:** To solve a rational equation, multiply both sides by the denominator to eliminate the fraction, but remember to check for values that make the denominator zero (excluded values). 3. **Multiply both sides by the denominator:** $$\cancel{(x-3)} \cdot \frac{2x+4}{\cancel{x-3}} = 3 \cdot (x-3)$$ which simplifies to $$2x + 4 = 3(x - 3)$$ 4. **Expand the right side:** $$2x + 4 = 3x - 9$$ 5. **Bring all terms to one side:** $$2x + 4 - 3x + 9 = 0$$ which simplifies to $$-x + 13 = 0$$ 6. **Solve for $x$:** $$-x = -13$$ $$x = 13$$ 7. **Check for excluded values:** The denominator $x-3$ cannot be zero, so $x \neq 3$. Since $x=13$ is allowed, it is the solution. **Final answer:** $$x = 13$$