This image contains two mathematical questions written in Persian, which involve simplification and evaluation of expressions with square roots. Here's a breakdown and solution for each question:

1st Question:

The first question asks for the simplified result of the expression:

$\frac{6}{\sqrt{3}} - \frac{2}{\sqrt{3} + 1}$

Steps:

1. Simplify the term $\frac{6}{\sqrt{3}}$:
   Multiply numerator and denominator by $\sqrt{3}$ to rationalize:
   $\frac{6}{\sqrt{3}} = \frac{6 \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}} = \frac{6\sqrt{3}}{3} = 2\sqrt{3}$

2. Simplify the term $\frac{2}{\sqrt{3} + 1}$:
   Multiply numerator and denominator by $\sqrt{3} - 1$ to rationalize:
   $\frac{2}{\sqrt{3} + 1} \cdot \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{2(\sqrt{3} - 1)}{(\sqrt{3} + 1)(\sqrt{3} - 1)}$
   The denominator simplifies as follows (difference of squares):
   $(\sqrt{3})^2 - (1)^2 = 3 - 1 = 2$
   Therefore:
   $\frac{2}{\sqrt{3} + 1} = \frac{2(\sqrt{3} - 1)}{2} = \sqrt{3} - 1$

3. Combine the terms:
   $\frac{6}{\sqrt{3}} - \frac{2}{\sqrt{3} + 1} = 2\sqrt{3} - (\sqrt{3} - 1)$
   Distribute the negative sign:
   $2\sqrt{3} - \sqrt{3} + 1 = \sqrt{3} + 1$

Final Answer:

The result simplifies to $\sqrt{3} + 1$. The correct option is (4).

2nd Question:

The second question asks for the result of:

$\frac{7}{\sqrt{2}} + \frac{1}{\sqrt{3} + \sqrt{2}}$

Steps:

1. Simplify the term $\frac{7}{\sqrt{2}}$:
   Multiply numerator and denominator by $\sqrt{2}$:
   $\frac{7}{\sqrt{2}} = \frac{7\sqrt{2}}{2}$

2. Simplify the term $\frac{1}{\sqrt{3} + \sqrt{2}}$:
   Multiply numerator and denominator by $\sqrt{3} - \sqrt{2}$ to rationalize:
   $\frac{1}{\sqrt{3} + \sqrt{2}} \cdot \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}} = \frac{\sqrt{3} - \sqrt{2}}{(\sqrt{3})^2 - (\sqrt{2})^2}$
   The denominator simplifies as follows (difference of squares):
   $(\sqrt{3})^2 - (\sqrt{2})^2 = 3 - 2 = 1$
   Therefore:
   $\frac{1}{\sqrt{3} + \sqrt{2}} = \sqrt{3} - \sqrt{2}$

3. Combine the terms:
   $\frac{7}{\sqrt{2}} + \frac{1}{\sqrt{3} + \sqrt{2}} = \frac{7\sqrt{2}}{2} + (\sqrt{3} - \sqrt{2})$

This is not easily simplified further without numerical evaluation, but the expression involves terms combining $\sqrt{2}$ and $\sqrt{3}$.

Final Answers:

1. First question answer: Option (4) — $\sqrt{3} + 1$
2. Second question: Requires precise evaluation. Option involving radicals.

Would you like a deeper step-by-step explanation for the second question or further simplifications? Let me know!

Related Questions:

1. How do you rationalize denominators involving two radicals?
2. What is the difference of squares, and how is it used in simplifications?
3. Can you simplify $\frac{a}{\sqrt{b} + \sqrt{c}}$ generally?
4. How do you combine like terms with square roots?
5. How do you evaluate square root expressions numerically?

Tip: Always rationalize square root expressions in denominators to make them easier to manipulate and compare.