• # question_answer Find the value of the given expression$2+\frac{1}{\sqrt{2}}+\frac{1}{2+\sqrt{2}}+\frac{1}{\sqrt{2}-2}$? A)  $2+\frac{1}{\sqrt{2}}$           B)  $-\frac{1}{\sqrt{2}}$C)  $2-\frac{1}{\sqrt{2}}$ D)  $\frac{1}{\sqrt{2}}$

(c): Rationalizing, we get $2+\frac{\sqrt{2}}{2}+\frac{2-\sqrt{2}}{2}+\frac{2+\sqrt{2}}{-2}$ $=2+\frac{\cancel{\sqrt{2}}+\cancel{\sqrt{2}}-\cancel{\sqrt{2}}-2-\sqrt{2}}{2}$ $=2-\frac{\sqrt{2}}{2}=2-\frac{1}{\sqrt{2}}$.