Question

Упростите выражение:

Answer 1

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

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

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

Ответ: $frac{134}{31}$