To rationalize the denominator of the expression $\frac{3}{\sqrt{3} - 2}$, follow these steps:

Step 1: Multiply by the conjugate

To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of $\sqrt{3} - 2$ is $\sqrt{3} + 2$.

$\frac{3}{\sqrt{3} - 2} \times \frac{\sqrt{3} + 2}{\sqrt{3} + 2} = \frac{3(\sqrt{3} + 2)}{(\sqrt{3} - 2)(\sqrt{3} + 2)}$

Step 2: Simplify the denominator

The denominator is a difference of squares:

$(\sqrt{3})^2 - 2^2 = 3 - 4 = -1$

Step 3: Simplify the numerator

Distribute the $3$ across the terms in the numerator:

$3(\sqrt{3} + 2) = 3\sqrt{3} + 6$

Step 4: Combine the results

Now, put it all together:

$\frac{3\sqrt{3} + 6}{-1} = -3\sqrt{3} - 6$

So, the simplified expression is $\boxed{-3\sqrt{3} - 6}$.

Would you like any more details or have any further questions? Here are some related questions:

1. What is the importance of using the conjugate when rationalizing denominators?
2. How do you apply the difference of squares formula in different contexts?
3. Can you rationalize the denominator of $\frac{5}{\sqrt{2} - 1}$?
4. What are the properties of conjugates and how do they help in simplifications?
5. How would the process change if the denominator was $\sqrt{3} + 2$ instead?

Tip: Rationalizing denominators helps in simplifying expressions and making them easier to work with, especially when dealing with square roots!