1. Simplify: \[ \frac{\sqrt{5}}{\sqrt{3} + \sqrt{2}} - \frac{3\sqrt{3}}{\sqrt{2} + \sqrt{5}} + \frac{2\sqrt{2}}{\sqrt{3} + \sqrt{5}} \]

2. Simplify: \[ \frac{3\sqrt{7}}{\sqrt{5} + \sqrt{2}} - \frac{5\sqrt{5}}{\sqrt{2} + \sqrt{7}} + \frac{2\sqrt{2}}{\sqrt{7} + \sqrt{5}} \]

3. Simplify: \[ \frac{3\sqrt{7}}{\sqrt{2} + \sqrt{5}} - \frac{5\sqrt{5}}{\sqrt{2} + \sqrt{7}} + \frac{2\sqrt{2}}{\sqrt{5} + \sqrt{7}} \]

4. Find the simplest value of the following expression: \[ \cfrac{\sqrt{5}}{\sqrt{3}+\sqrt{2}} - \cfrac{3\sqrt{3}}{\sqrt{2}+\sqrt{5}} + \cfrac{2\sqrt{2}}{\sqrt{3}+\sqrt{5}} \]

5. Simplify: \[ \frac{3\sqrt{7}}{\sqrt{5} + \sqrt{2}} - \frac{5\sqrt{5}}{\sqrt{2} + \sqrt{7}} + \frac{2\sqrt{2}}{\sqrt{7} + \sqrt{5}} \]

6. If \[ x = \frac{2\sqrt{15}}{\sqrt{5} + \sqrt{3}} \] then find the value of \[ \frac{x + \sqrt{3}}{x - \sqrt{3}} + \frac{x + \sqrt{5}}{x - \sqrt{5}} \]

7. Find the simplest value of: \[ \cfrac{2\sqrt{7}}{\sqrt{5} + \sqrt{3}} + \cfrac{2\sqrt{3}}{\sqrt{7} + \sqrt{5}} - \cfrac{4\sqrt{5}}{\sqrt{7} + \sqrt{3}} \]

8. The simplest value of \[ \frac{1}{\sqrt{1} + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \ldots + \frac{1}{\sqrt{99} + \sqrt{100}} \] is —

(a) 100 (b) 99 (c) 9 (d) 1

9. Simplify: \[ \frac{1}{\sqrt{2} + \sqrt{3}} - \frac{\sqrt{3} + 1}{2 + \sqrt{3}} + \frac{\sqrt{2} + 1}{3 + 2\sqrt{2}} \]

10. Let us evaluate the value of: \(\cfrac{8+3\sqrt{2}}{3+\sqrt{5}}-\cfrac{8-3\sqrt{2}}{3-\sqrt{5}}\)

11. Simplify: \[ \frac{3\sqrt{2}}{\sqrt{3} + \sqrt{6}} - \frac{4\sqrt{3}}{\sqrt{6} + \sqrt{2}} + \frac{\sqrt{6}}{\sqrt{2} + \sqrt{3}} \]

12. Determine the simplest value of \[ \left(\frac{1}{\sqrt{2}+1} + \frac{1}{\sqrt{3}+\sqrt{2}} + \frac{1}{\sqrt{4}+\sqrt{3}}\right) \]