The value of $$\frac{2\sqrt{10}}{\sqrt{5} + \sqrt{2} - \sqrt{7}} - \sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2}} - \frac{3}{\sqrt{7} - 2}$$ is:

let the A = $$\frac{2\sqrt{10}}{\sqrt{5} + \sqrt{2}- \sqrt{7}}, B = \sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2}} and C = \frac{3}{\sqrt{7} - 2}$$.

C =$$\frac{3}{\sqrt{7} - 2}$$ 

multiply and divide by $$\sqrt{7} + 2$$

C = $$\frac{3}{\sqrt{7} - 2} \frac{\sqrt{7} + 2}{\sqrt{7} + 2}$$

by using (a+b)(a-b) = $$a^2 - b^2$$

C = $$\frac{3\sqrt{7} + 6}{3} = \sqrt{7} + 2$$

B = $$\sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2}}$$

multiply and divide by $$\sqrt{5} - 2$$

B = $$\sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2} \times \frac{\sqrt{5} - 2}{\sqrt{5} - 2}} = \sqrt{(\sqrt{5} - 2)^2} = \sqrt{5} - 2 $$

A = $$\frac{2\sqrt{10}}{(\sqrt{5} + \sqrt{2})- \sqrt{7}}$$

divide and multiply by $$(\sqrt{5} + \sqrt{2}) +  \sqrt{7}$$

A = $$\frac{2\sqrt{10}}{(\sqrt{5} + \sqrt{2})- \sqrt{7}} \times \frac{(\sqrt{5} + \sqrt{2}) + \sqrt{7}}{(\sqrt{5} + \sqrt{2}) + \sqrt{7}}$$

= $$\frac{2\sqrt{10} \times [\sqrt{5}+\sqrt{2}+\sqrt{7}]}{(\sqrt{5}+\sqrt{2})^2-7}$$

= $$\frac{2\sqrt{10} \times [\sqrt{5}+\sqrt{2}+\sqrt{7}]}{5 + 2 + 2\sqrt{10}-7}$$

= $$ [\sqrt{5}+\sqrt{2}+\sqrt{7}]$$

$$\frac{2\sqrt{10}}{\sqrt{5} + \sqrt{2} - \sqrt{7}} - \sqrt{\frac{\sqrt{5} - 2}{\sqrt{5} + 2}} - \frac{3}{\sqrt{7} - 2}$$

= A - B - C = $$ [\sqrt{5}+\sqrt{2}+\sqrt{7}] - \sqrt{5} + 2 - \sqrt{7} - 2 = \sqrt{2}$$