The problem asks to simplify the expression:

$\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$

To simplify this, we will multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{3} - \sqrt{2}$.

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

Now, simplify both the numerator and the denominator.

1. Denominator: $(\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1$ So the denominator simplifies to 1.

2. Numerator: $(\sqrt{3} - \sqrt{2})^2 = (\sqrt{3})^2 - 2(\sqrt{3})(\sqrt{2}) + (\sqrt{2})^2 = 3 - 2\sqrt{6} + 2$ Simplify the numerator: $3 - 2\sqrt{6} + 2 = 5 - 2\sqrt{6}$

Thus, the simplified form of the expression is:

$5 - 2\sqrt{6}$

The correct answer is (c) 5 - 2\sqrt{6}.

Would you like a detailed explanation or have any other questions?

Here are 5 related questions for further practice:

1. How do you rationalize the denominator of a fraction involving square roots?
2. What are conjugates, and how are they used to simplify expressions?
3. How do you simplify a binomial squared that involves square roots?
4. Can you simplify the expression $\frac{1}{\sqrt{5} + \sqrt{3}}$?
5. How do you expand $(\sqrt{a} - \sqrt{b})^2$ for general values of $a$ and $b$?

Tip: Multiplying by the conjugate is a common technique to eliminate square roots from denominators. Always check if this approach simplifies the expression efficiently.