Answer 1

$\frac{7-3\sqrt{2}}{7+3\sqrt{2}}+\frac{7+3\sqrt{2}}{7-3\sqrt{2}}=\\ \frac{(7-3\sqrt{2})^2+(7+3\sqrt{2})^2}{49-18}=\frac{49-42\sqrt{2}+18+49+42\sqrt{2}+18}{31}=\frac{98+36}{31}=\frac{134}{31}=4\frac{10}{31}$

Answer 2

$\frac{7-3 \sqrt{2} }{7+3 \sqrt{2} } + \frac{7+3 \sqrt{2} }{7-3 \sqrt{2} } = \frac{(7-3 \sqrt{2})^2 }{7^2- (\sqrt{18})^2 } + \frac{(7+3 \sqrt{2})^2 }{7^2- (\sqrt{18})^2 } = \frac{49-14 \sqrt{18}+18+49+14 \sqrt{18+18} }{49-18} = \frac{134}{31} =4 \frac{10}{31}$

Answer 3

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