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 to isolate $x$ terms on one side: $$2x + 4 - 3x = 6$$ $$\cancel{2x} + 4 - \cancel{3x} = 6$$ which simplifies to: $$-x + 4 = 6$$ 6. Subtract 4 from both sides: $$-x + 4 - 4 = 6 - 4$$ $$-x = 2$$ 7. Multiply both sides by $-1$ to solve for $x$: $$x = -2$$ 8. Check the denominator $x+2$ for $x = -2$: $$-2 + 2 = 0$$ Since the denominator is zero, $x = -2$ is not allowed. 9. Therefore, the equation has no solution. Final answer: No solution because $x = -2$ makes the denominator zero.