Упр.2.153 ГДЗ Дорофеев Суворова 8 класс (Алгебра)

а) 1/(v6+v5)+1/(v6-v5);
б) (v3-v2)/(v3+v2)-(v3+v2)/(v3-v2).

а)

$$ \frac{1}{\sqrt{6}+\sqrt{5}}+\frac{1}{\sqrt{6}-\sqrt{5}} = \frac{\sqrt{6}-\sqrt{5}}{(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5})} + \frac{\sqrt{6}+\sqrt{5}}{(\sqrt{6}-\sqrt{5})(\sqrt{6}+\sqrt{5})} $$

$$ = \frac{\sqrt{6}-\sqrt{5}+\sqrt{6}+\sqrt{5}}{6-5} = \frac{2\sqrt{6}}{1} = 2\sqrt{6} $$

б)

$$ \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}-\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}} = \frac{(\sqrt{3}-\sqrt{2})^2-(\sqrt{3}+\sqrt{2})^2}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})} $$

$$ = \frac{(3-2\sqrt{6}+2)-(3+2\sqrt{6}+2)}{3-2} = \frac{5-2\sqrt{6}-5-2\sqrt{6}}{1} = -4\sqrt{6} $$

Ответ

а) $$2\sqrt{6}$$; б) $$-4\sqrt{6}$$.