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

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

= $$(\frac{3\sqrt{7}}{\sqrt{5}+\sqrt{2}}\times\frac{\sqrt5-\sqrt2}{\sqrt5-\sqrt2})-(\frac{5\sqrt{5}}{\sqrt{7}+\sqrt{2}}\times\frac{\sqrt7-\sqrt2}{\sqrt7-\sqrt2})+(\frac{2\sqrt{2}}{\sqrt{7}+\sqrt{5}}\times\frac{\sqrt7-\sqrt5}{\sqrt7-\sqrt5})$$

Using, $$(a+b)(a-b)=a^2-b^2$$

= $$\frac{3\sqrt{7}(\sqrt{5}-\sqrt{2})}{5-2}-\frac{5\sqrt{5}(\sqrt{7}-\sqrt{2})}{7-2}+\frac{2\sqrt{2}(\sqrt{7}-\sqrt{5})}{7-5}$$

= $$\frac{3\sqrt{7}(\sqrt{5}-\sqrt{2})}{3}-\frac{5\sqrt{5}(\sqrt{7}-\sqrt{2})}{5}+\frac{2\sqrt{2}(\sqrt{7}-\sqrt{5})}{2}$$

= $$\sqrt7(\sqrt5-\sqrt2)-\sqrt5(\sqrt7-\sqrt2)+\sqrt2(\sqrt7-\sqrt5)$$

= $$\sqrt{35}-\sqrt{14}-\sqrt{35}+\sqrt{10}+\sqrt{14}-\sqrt{10}=0$$

=> Ans - (B)