1. The problem is to solve the equation $$\frac{2x+4}{x+2} = 3$$ for $x$. 2. We start by stating the 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. 3. Multiply both sides by $x+2$: $$\cancel{\frac{2x+4}{x+2}} \times (x+2) = 3 \times (x+2)$$ which simplifies to: $$2x + 4 = 3(x + 2)$$ 4. Expand the right side: $$2x + 4 = 3x + 6$$ 5. Rearrange terms to isolate $x$: $$2x + 4 - 3x = 6$$ $$-x + 4 = 6$$ 6. Subtract 4 from both sides: $$-x + \cancel{4} - \cancel{4} = 6 - 4$$ $$-x = 2$$ 7. Multiply both sides by $-1$ to solve for $x$: $$x = -2$$ 8. Check the denominator for $x = -2$: Denominator is $x + 2 = -2 + 2 = 0$, which is undefined. 9. Since $x = -2$ makes the denominator zero, it is not a valid solution. 10. Therefore, the equation has \textbf{no solution}.