1. **State the problem:** Solve the equation $$\frac{5}{2x + 1} = \frac{3}{x + 3}$$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products are equal. So, $$5(x + 3) = 3(2x + 1)$$ 3. **Expand both sides:** $$5x + 15 = 6x + 3$$ 4. **Bring all terms involving $x$ to one side and constants to the other:** $$5x + 15 = 6x + 3$$ $$5x - 6x = 3 - 15$$ $$-x = -12$$ 5. **Divide both sides by $-1$ to solve for $x$:** $$\cancel{-1} \cdot x = \cancel{-1} \cdot 12$$ $$x = 12$$ 6. **Check for restrictions:** The denominators cannot be zero. - For $2x + 1 \neq 0$, $x \neq -\frac{1}{2}$ - For $x + 3 \neq 0$, $x \neq -3$ Since $x=12$ does not violate these, it is a valid solution. **Final answer:** $$x = 12$$