1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-1} = 3$$ 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 $x \neq 1$ because the denominator cannot be zero. 3. **Multiply both sides by $x-1$: ** $$\cancel{\frac{2x+4}{\cancel{x-1}}} \times \cancel{x-1} = 3 \times (x-1)$$ which simplifies to $$2x + 4 = 3(x - 1)$$ 4. **Expand the right side:** $$2x + 4 = 3x - 3$$ 5. **Bring all terms to one side to isolate $x$: ** $$2x + 4 - 3x + 3 = 0$$ which simplifies to $$-x + 7 = 0$$ 6. **Solve for $x$: ** $$-x = -7$$ $$x = 7$$ 7. **Check for restrictions:** Since $x=7$ does not make the denominator zero, it is a valid solution. **Final answer:** $$x = 7$$