https://file.aiquickdraw.com/mathbot/file/1727224013139waerjbib.jpg

The expression in the image is:

\[
\frac{3\sqrt{2}}{\sqrt{5} - \sqrt{2}}
\]

To simplify this, we can multiply both the numerator and the denominator by the conjugate of the denominator, which is \( \sqrt{5} + \sqrt{2} \). This will eliminate the square roots in the denominator.

### Step 1: Multiply by the conjugate

\[
\frac{3\sqrt{2}}{\sqrt{5} - \sqrt{2}} \times \frac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}} = \frac{3\sqrt{2}(\sqrt{5} + \sqrt{2})}{(\sqrt{5})^2 - (\sqrt{2})^2}
\]

### Step 2: Simplify the denominator

The denominator simplifies to:

\[
(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3
\]

### Step 3: Simplify the numerator

Now, expand the numerator:

\[
3\sqrt{2}(\sqrt{5} + \sqrt{2}) = 3\sqrt{2} \cdot \sqrt{5} + 3\sqrt{2} \cdot \sqrt{2}
\]

This gives:

\[
3\sqrt{10} + 3 \times 2 = 3\sqrt{10} + 6
\]

### Step 4: Combine everything

Now, the expression becomes:

\[
\frac{3\sqrt{10} + 6}{3}
\]

Simplifying by dividing both terms in the numerator by 3:

\[
\sqrt{10} + 2
\]

Thus, the simplified form is:

\[
2 + \sqrt{10}
\]

So, the correct answer is **A. 2 + \(\sqrt{10}\)**.

Would you like more details or further clarification?

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Here are 5 related questions for practice:

1. Simplify \( \frac{\sqrt{3} + \sqrt{5}}{\sqrt{3} - \sqrt{5}} \).
2. How do you rationalize the denominator in an expression like \( \frac{1}{\sqrt{7} - \sqrt{3}} \)?
3. Simplify \( \frac{5}{\sqrt{2}} \).
4. What is the result of multiplying \( (\sqrt{7} + 2)(\sqrt{7} - 2) \)?
5. How do you simplify \( \frac{4}{\sqrt{2} + 1} \)?

**Tip:** Always look to multiply by the conjugate when simplifying expressions with square roots in the denominator.

Bentuk sederhana dari (3√2) / (√5 - √2) adalah?

This detailed guide explains how to simplify the expression (3√2) / (√5 - √2) by multiplying by the conjugate. Learn key concepts such as rationalizing denominators and simplifying square roots. Perfect for high school students in Grades 10-12.

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