Question

избавьте от иррациональности в знаменателе 3/(2-√2+√3-√6)

Answer 1

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

$=frac{3}{(sqrt{2}-sqrt{3})*(sqrt{2} -1)}=$

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

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

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

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