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?

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.