1. **Problem Statement:** Solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Formula and Rules:** To solve rational equations, multiply both sides by the denominator to eliminate the fraction, but remember to check for values that make the denominator zero (excluded values). 3. **Step 1: Identify excluded values.** The denominator $x-3$ cannot be zero, so $x \neq 3$. 4. **Step 2: Multiply both sides by $x-3$ to clear the fraction:** $$\cancel{\frac{2x+4}{x-3}} \times (x-3) = 3 \times (x-3)$$ which simplifies to $$2x + 4 = 3(x - 3)$$ 5. **Step 3: Expand the right side:** $$2x + 4 = 3x - 9$$ 6. **Step 4: Rearrange terms to isolate $x$:** $$2x + 4 - 3x = -9$$ $$-x + 4 = -9$$ 7. **Step 5: Subtract 4 from both sides:** $$-x = -9 - 4$$ $$-x = -13$$ 8. **Step 6: Multiply both sides by $-1$ to solve for $x$:** $$\cancel{-1} \times (-x) = \cancel{-1} \times (-13)$$ $$x = 13$$ 9. **Step 7: Check the solution against excluded values:** $x=13$ is not excluded, so it is valid. **Final answer:** $$x = 13$$