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 it makes the denominator 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 to one side to isolate $x$:** $$2x + 4 - 3x + 9 = 0$$ which simplifies to $$-x + 13 = 0$$ 6. **Solve for $x$:** $$-x = -13$$ $$x = 13$$ 7. **Check for restrictions:** Since $x = 13$ does not make the denominator zero, it is a valid solution. **Final answer:** $$x = 13$$