1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-1} = 3$$ 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. **Identify excluded values:** The denominator is $x-1$, so $x \neq 1$. 4. **Multiply both sides by $x-1$:** $$\cancel{\frac{2x+4}{x-1}} \times (x-1) = 3 \times (x-1)$$ which simplifies to $$2x + 4 = 3(x - 1)$$ 5. **Expand the right side:** $$2x + 4 = 3x - 3$$ 6. **Bring all terms to one side:** $$2x + 4 - 3x + 3 = 0$$ which simplifies to $$-x + 7 = 0$$ 7. **Solve for $x$:** $$-x = -7$$ $$x = 7$$ 8. **Check excluded values:** $x=7$ is not excluded, so it is a valid solution. **Final answer:** $$x = 7$$