Question

Избавьтесь от иррациональности в знаменателе $\frac{1}{\sqrt{3}-\sqrt{5}-2\sqrt{2} }$

Answer 1

$\frac{1}{\sqrt3-\sqrt5-2\sqrt2}=\frac{(\sqrt3-\sqrt5)+2\sqrt2}{(\sqrt3-\sqrt5)^2-(2\sqrt2)^2}=\frac{\sqrt3-\sqrt5+2\sqrt2}{(8-2\sqrt{15})-8}=-\frac{\sqrt3-\sqrt5+2\sqrt2}{2\sqrt{15}} =\\\\=-\frac{(\sqrt3-\sqrt5+2\sqrt2)\cdot \sqrt{15}}{30}=\frac{-\sqrt{3\cdot 15}+\sqrt{5\cdot 15}-2\sqrt{2\cdot 15}}{30}=\frac{5\sqrt3-3\sqrt5-2\sqrt{30}}{30}$