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. **Identify excluded values:** The denominator $x-3$ cannot be zero, so $x \neq 3$. 4. **Multiply both sides by $x-3$:** $$\cancel{\frac{2x+4}{x-3}} \times (x-3) = 3 \times (x-3)$$ which simplifies to $$2x + 4 = 3(x - 3)$$ 5. **Expand the right side:** $$2x + 4 = 3x - 9$$ 6. **Bring all terms to one side:** $$2x + 4 - 3x + 9 = 0$$ which simplifies to $$-x + 13 = 0$$ 7. **Solve for $x$:** $$-x + 13 = 0 \implies -x = -13 \implies x = 13$$ 8. **Check excluded values:** $x=13$ is not excluded, so it is a valid solution. **Final answer:** $$x = 13$$