What is the value of $$(2+\sqrt{2})+\left(\frac{1}{2+\sqrt{2}}\right)+\left(\frac{1}{2-\sqrt{2}}\right)+(2-\sqrt{2})$$?
$$(2+\sqrt{2})+\left(\frac{1}{2+\sqrt{2}}\right)+\left(\frac{1}{2-\sqrt{2}}\right)+(2-\sqrt{2})$$
$$=(2+\sqrt{2})+\left(\frac{2-\sqrt{2}}{4-2}\right)+\left(\frac{2+\sqrt{2}}{4-2}\right)+(2-\sqrt{2})$$
$$=\left(2+2\right)+\left(\frac{2-\sqrt{2}+2+\sqrt{2}}{2}\right)\ .$$
$$=4+\left(\frac{4}{2}\right)\ .$$
$$=6\ .$$
D is correct choice.
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