Question

Упростить выражение $frac{sqrt{3}-sqrt{2}}{sqrt{3}+sqrt{2}}$

Answer 1

$frac{sqrt{3}-sqrt{2}}{sqrt{3}+sqrt{2}}=frac{(sqrt{3}-sqrt{2})(sqrt{3}-sqrt{2})}{(sqrt{3}+sqrt{2})(sqrt{3}-sqrt{2})}=\\=frac{(sqrt{3})^2-2sqrt{2}*sqrt{3}+(sqrt{2})^2}{(sqrt{3})^2-(sqrt{2})^2}=\\=frac{3-2sqrt{6}+2}{3-2}=frac{5-2sqrt{6}}{1}=5-2sqrt{6}$