A) 0
B) \[2\sqrt{15}\]
C) \[2\sqrt{10}\]
D) \[2\sqrt{6}\]
Correct Answer: A
Solution :
\[\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}}-\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}}+\frac{2\sqrt{2}}{\sqrt{5}+\sqrt{3}}\] \[=\frac{\sqrt{5}(\sqrt{3}-\sqrt{2})}{3-2}-\frac{3\sqrt{3}(\sqrt{5}-\sqrt{2})}{5-2}+\frac{2\sqrt{2}(\sqrt{5}+\sqrt{3})}{5-3}\]\[=\sqrt{15}-\sqrt{10}-\sqrt{15}+\sqrt{6}+\sqrt{10}-\sqrt{6}\] = 0
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