Question

Помогите упростить выражение

Answer 1

$\displaystyle\tt \ \ \ \frac{\sqrt{6}- \sqrt{3}- \sqrt{2}+1}{\sqrt{10}-\sqrt{5}+\sqrt{2}-1} =\frac{\sqrt{3}\cdot\sqrt{2}-\sqrt{3}-\sqrt{2}+1}{\sqrt{5}\cdot\sqrt{2}-\sqrt{5}+\sqrt{2}-1}=\\\\\\=\frac{\sqrt{3}(\sqrt{2}-1)-(\sqrt{2}-1)}{\sqrt{5}(\sqrt{2}-1)+(\sqrt{2}-1)}=\frac{(\sqrt{2}-1)(\sqrt{3}-1)}{(\sqrt{2}-1)(\sqrt{5}+1)}=\frac{\sqrt{3}-1}{\sqrt{5}+1}$