1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both sides by the denominator to eliminate the fraction, but remember $x \neq 3$ because the denominator cannot be zero. 3. **Multiply both sides by $x-3$: $$\cancel{\frac{2x+4}{x-3}} \times (x-3) = 3 \times (x-3)$$ which simplifies to $$2x+4 = 3(x-3)$$** 4. **Expand the right side:** $$2x + 4 = 3x - 9$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$2x - 3x = -9 - 4$$ which simplifies to $$-x = -13$$ 6. **Divide both sides by $-1$: $$\cancel{-x} \div \cancel{-1} = \frac{-13}{-1}$$ giving $$x = 13$$** 7. **Check the solution:** Substitute $x=13$ back into the denominator $x-3 = 13-3=10 \neq 0$, so $x=13$ is valid. **Final answer:** $$x = 13$$