Question

Упростите выражение:

Answer 1

$\frac{7-3\sqrt{2}}{7+3\sqrt{2}}+\frac{7+3\sqrt{2}}{7-3\sqrt{3}}= \frac{(7+3\sqrt{2})-6\sqrt{2}}{7+3\sqrt{2}}+\frac{(7-3\sqrt{2})+6\sqrt{2}}{7-3\sqrt{2}}=1-\frac{6\sqrt{2}}{7+3\sqrt{2}}+1+\frac{6\sqrt{2}}{7-3\sqrt{2}}$

$=2+6\sqrt{2}\left(\frac{1}{7-3\sqrt{2}}-\frac{1}{7+3\sqrt{2}}\right)= 2+6\sqrt{2}\frac{(7+3\sqrt{2})-(7-3\sqrt{2})}{(7-3\sqrt{2})(7+3\sqrt{2})}=2+\frac{6\sqrt{2}\cdot 6\sqrt{2}}{49-18}$

$=2+\frac{72}{31}=\frac{62+72}{31}=\frac{134}{31}$

Ответ: $\frac{134}{31}$