Question

Алгебра 10 класс. Фото

Answer 1

$1)\; \; \; \frac{1}{2-\sqrt3}-\frac{1}{\sqrt3-\sqrt2}+\frac{1}{\sqrt2-1}=\\\\=\frac{2+\sqrt3}{(2-\sqrt3)(2+\sqrt3)}-\frac{\sqrt3+\sqrt2}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}+\frac{\sqrt2+1}{(\sqrt2-1)(\sqrt2+1)}=\\\\=\frac{2+\sqrt3}{4-3}-\frac{\sqrt3+\sqrt2}{3-2}+\frac{\sqrt2+1}{2-1}=2+\sqrt3-\sqrt3-\sqrt2+\sqrt2+1=2+1=3\\\\2)\; \; \; \frac{1}{3-\sqrt8}-\frac{1}{\sqrt8-\sqrt7}+\frac{6}{\sqrt7-1}=\\\\=\frac{3+\sqrt8}{9-8}-\frac{\sqrt8+\sqrt7}{8-7}+\frac{6(\sqrt7+1)}{7-1}=3+\sqrt8-\sqrt8-\sqrt7+\sqrt7+1=3+1=4$