A) 2
B) \[2-\sqrt{2}\]
C) \[4+\sqrt{2}\]
D) \[2\sqrt{2}\]
Correct Answer: A
Solution :
\[2+\sqrt{2}+\frac{1}{2+\sqrt{2}}-\frac{1}{2-\sqrt{2}}\] \[=2+\sqrt{2}+\frac{2-\sqrt{2}-2-\sqrt{2}}{4-2}\] \[=2+\sqrt{2}+\frac{(-2\sqrt{2})}{2}\] \[=2+\sqrt{2}-\sqrt{2}=2\]
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