Question

Освободитесь от иррациональности в знаменателе дроби:
$frac{6}{sqrt{10}+sqrt{6}+5-sqrt{15}}$

Answer 1

$frac{6}{sqrt{10}+sqrt{6}+5-sqrt{15}} = frac{6}{(sqrt{10}+sqrt{6}) + (5-sqrt{15})} = \ \ \ = frac{6}{(sqrt{10}+sqrt{6}) + (5-sqrt{15})} * frac{(sqrt{10}+sqrt{6}) - (5-sqrt{15})}{(sqrt{10}+sqrt{6}) - (5-sqrt{15})} = \ \ \ = frac{6((sqrt{10}+sqrt{6}) - (5-sqrt{15}))}{(sqrt{10}+sqrt{6})^2 - (5-sqrt{15})^2} = \ \ \ = frac{6((sqrt{10}+sqrt{6}) - (5-sqrt{15}))}{(16+2sqrt{60}) - (40-10sqrt{15})} =$

$= frac{6(sqrt{10}+sqrt{6} -5+sqrt{15})}{14sqrt{15} - 24} = \ \ \ = frac{6(sqrt{10}+sqrt{6} -5+sqrt{15})}{14sqrt{15} - 24} * frac{{14 sqrt{15} + 24}}{14 sqrt{15} + 24}} = \ \ \ = frac{6(sqrt{10}+sqrt{6} -5+sqrt{15})*({14 sqrt{15} + 24})}{(14sqrt{15})^2 - 24^2} =$

$= frac{6(sqrt{10}+sqrt{6} -5+sqrt{15})*({14 sqrt{15} + 24})}{2364}$