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:** $$ (x-3) \times \frac{2x+4}{x-3} = 3 \times (x-3) $$ 4. **Simplify by canceling the denominator:** $$ \cancel{(x-3)} \times \frac{2x+4}{\cancel{(x-3)}} = 3(x-3) $$ $$ 2x + 4 = 3x - 9 $$ 5. **Isolate $x$ terms on one side:** $$ 2x + 4 = 3x - 9 $$ $$ 4 + 9 = 3x - 2x $$ $$ 13 = x $$ 6. **Check for excluded values:** Denominator $x-3 \neq 0 \Rightarrow x \neq 3$. Since $x=13$ is not excluded, it is a valid solution. **Final answer:** $$ x = 13 $$