Simplify the following expression as much as possible:

$$
\sqrt{\frac{2-\sqrt{2}}{2+\sqrt{2}}}+\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}
$$
After rationalizing the denominators under the square roots:

$$
\sqrt{\frac{(2-\sqrt{2})^{2}}{4-2}}+\sqrt{\frac{(2+\sqrt{2})^{2}}{4-2}}=\frac{2-\sqrt{2}}{\sqrt{2}}+\frac{2+\sqrt{2}}{\sqrt{2}}=\frac{4}{\sqrt{2}}=2 \sqrt{2}
$$

Barnabás Takács (Kecskemét, J. Katona II. Grammar School)