Which expression is equivalent to \( \frac{c^{2}-4}{c+3} \div \frac{c+2}{3\left(c^{2}-9\right)} ? \) \( \frac{c+3}{c^{2}-4} \div \frac{c+2}{3\left(c^{2}-9\right)} \) \( \frac{c^{2}-4}{c+3} \div \frac{3\left(c^{2}-9\right)}{c+2} \) \( \frac{c^{2}-4}{c+3} \cdot \frac{3\left(c^{2}-9\right)}{c+2} \) \( \frac{c+3}{c^{2}-4} \cdot \frac{c+2}{3\left(c^{2}-9\right)} \)

To solve the original expression, we start by recalling how division of fractions works: dividing by a fraction is the same as multiplying by its reciprocal. Our expression changes from: \[ \frac{c^{2}-4}{c+3} \div \frac{c+2}{3\left(c^{2}-9\right)} \] to: \[ \frac{c^{2}-4}{c+3} \cdot \frac{3\left(c^{2}-9\right)}{c+2} \] Thus, the equivalent expression is \( \frac{c^{2}-4}{c+3} \cdot \frac{3\left(c^{2}-9\right)}{c+2} \). This kind of manipulation is not just handy in math; it also makes solving equations and inequalities a piece of cake! Whenever you're dividing by a fraction, flip it over and multiply—the math gods will surely smile upon you. When dealing with expressions like this, it’s crucial to watch for potential simplifications. Always look for common factors in the numerator and denominator before multiplying, as this can save you from lengthy calculations. For instance, recognize that \(c^2 - 9\) factors to \((c - 3)(c + 3)\) and \(c^2 - 4\) factors as \((c - 2)(c + 2)\). Factor wherever possible to simplify your expressions early!