Question

Избавиться от иррациональности в знаменателе дроби

Answer 1

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Answer 2

$displaystyle tt frac{1}{sqrt{2}-sqrt{3}+sqrt{5}}=frac{sqrt{2}-sqrt{3}-sqrt{5}}{(sqrt{2}-sqrt{3}+sqrt{5})(sqrt{2}-sqrt{3}-sqrt{5})}=\\\ =frac{sqrt{2}-sqrt{3}-sqrt{5}}{(sqrt{2}-sqrt{3})^{2}-(sqrt{5})^{2}}=frac{sqrt{2}-sqrt{3}-sqrt{5}}{2-2sqrt{6}+3-5}=-frac{sqrt{2}-sqrt{3}-sqrt{5}}{2sqrt{6}}=\\\=-frac{sqrt{6}cdot (sqrt{2}-sqrt{3}-sqrt{5})}{12}=-frac{sqrt{12}-sqrt{18}-sqrt{30}}{12}=frac{sqrt{30}+3sqrt{2}-2sqrt{3}}{12};$