A) \[\sqrt{5}+\sqrt{6}\]
B) \[2\sqrt{5}+\sqrt{6}\]
C) \[\sqrt{5}-\sqrt{6}\]
D) \[2\sqrt{5}-3\sqrt{6}\]
Correct Answer: C
Solution :
Expression \[=\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}\] \[=\frac{(1+\sqrt{2})\,(\sqrt{5}-\sqrt{3})+(\sqrt{5}+\sqrt{3})(1-\sqrt{2})}{(\sqrt{5}+\sqrt{3})\,(\sqrt{5}-\sqrt{3})}\] \[=\frac{\sqrt{5}+\sqrt{10}-\sqrt{3}-\sqrt{6}+\sqrt{5}+\sqrt{3}-\sqrt{10}-\sqrt{6}}{5-3}\]\[=\frac{2\sqrt{5}-2\sqrt{6}}{2}=\frac{2\left( \sqrt{5}-\sqrt{6} \right)}{2}=\sqrt{5}-\sqrt{6}\]
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