Question

Va rog ajutati-ma.Simplificati fractia : Radical din 6 - Radical din 3 - radical din 2+1.Asupra Radical din 10- radical din 5+radical din 2 -1

Answer 1

   
[tex]\displaystyle \frac{ \sqrt{6}- \sqrt{3}-\sqrt{2}+1}{\sqrt{10}- \sqrt{5}+\sqrt{2}-1} = \\ \\ \\ =\frac{ (\sqrt{3\times2}- \sqrt{3})-(\sqrt{2}-1)}{(\sqrt{5\times2}- \sqrt{5})+(\sqrt{2}-1)} = \\ \\ \\ =\frac{ \sqrt{3}(\sqrt{2}- 1)-(\sqrt{2}-1)}{ \sqrt{5}(\sqrt{2}- 1)+(\sqrt{2}-1)} = \\ \\ \\ =\frac{ (\sqrt{2}- 1)(\sqrt{3}-1)}{ (\sqrt{2}- 1)(\sqrt{5}+1)} = ~~~se~simplifica~prin~(\sqrt{2}- 1) \\ \\ \\ =\boxed{\frac{ \sqrt{3}-1}{ \sqrt{5}+1}}[/tex]