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

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

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

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

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

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