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# 2^(1/2) + 1/(2 + 2^(1/2)) - 1/(2^(1/2) - 2) = ?

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Danou wrote:
$$\sqrt{2} +\frac{1}{2 + \sqrt{2}} + \frac{1}{\sqrt{2} - 2} =$$

A. $$0$$

B. $$2$$

C. $$\frac{\sqrt{2}}{2}$$

D. $$\sqrt{2}$$

E. $$2\sqrt{2}$$

$$\frac{1}{2 + \sqrt{2}} + \frac{1}{\sqrt{2} - 2}$$

$$\frac{\sqrt{2} - 2 + 2 + \sqrt{2}}{(2 + \sqrt{2})(\sqrt{2} - 2)}$$­

$$\frac{2\sqrt{2}}{2-4}$$­

$$\frac{-2\sqrt{2}}{2}$$­

$$-\sqrt{2}$$­

$$\sqrt{2} +\frac{1}{2 + \sqrt{2}} + \frac{1}{\sqrt{2} - 2} =$$

$$\sqrt{2} -\sqrt{2}$$

= 0

Option A

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