\[\frac{1^{\backslash 3 - 2\sqrt{2}}}{3 + 2\sqrt{2}} + \frac{1^{\backslash 3 + 2\sqrt{2}}}{3 - 2\sqrt{2}} =\]
\[= \frac{3 - 2\sqrt{2} + 3 + 2\sqrt{2}}{\left( 3 + 2\sqrt{2} \right)\left( 3 - 2\sqrt{2} \right)} =\]
\[= \frac{6}{9 - 4 \cdot 2} = 6.\]