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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.

Bentuk sederhana dari \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) adalah.....

Learn how to simplify the radical expression \(\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\) using the difference of squares and conjugates. This detailed step-by-step solution is suitable for students in Grades 9-11, covering key concepts in simplifying radical expressions and rationalizing denominators.

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