Упр.16.71 ГДЗ Мордкович 8 класс (Алгебра)

1. $$\frac{\sqrt z}{\sqrt{xy}}+\frac{\sqrt x}{\sqrt{yz}}=\frac{\sqrt z\cdot\sqrt{yz}+\sqrt x\cdot\sqrt{xy}}{\sqrt{xyz}}=\frac{\sqrt{yz^2}+\sqrt{xy^2}}{\sqrt{xyz}}=\frac{z+x}{\sqrt{xyz}}.$$

2. $$\frac{\sqrt m-\sqrt n}{\sqrt{mn}}+\frac{\sqrt m-\sqrt r}{\sqrt{nr}}=\frac{\sqrt r(\sqrt m-\sqrt n)+\sqrt m(\sqrt m-\sqrt r)}{\sqrt{mnr}}$$

   $$=\frac{\sqrt{mr}-\sqrt{nr}+m-\sqrt{mr}}{\sqrt{mnr}}=\frac{m-\sqrt{nr}}{\sqrt{mnr}}.$$

3. $$\frac{\sqrt m}{\sqrt{cd}}-\frac{\sqrt c}{\sqrt{dm}}=\frac{\sqrt m\cdot\sqrt m-\sqrt c\cdot\sqrt c}{\sqrt{cdm}}=\frac{m-c}{\sqrt{cdm}}.$$

4. $$\frac{\sqrt a+\sqrt b}{\sqrt{ab}}+\frac{\sqrt b-\sqrt c}{\sqrt{bc}}=\frac{\sqrt c(\sqrt a+\sqrt b)+\sqrt a(\sqrt b-\sqrt c)}{\sqrt{abc}}$$

   $$=\frac{\sqrt{ac}+\sqrt{bc}+\sqrt{ab}-\sqrt{ac}}{\sqrt{abc}}=\frac{\sqrt{bc}+\sqrt{ab}}{\sqrt{abc}}$$

   $$=\frac{\sqrt b(\sqrt c+\sqrt a)}{\sqrt{abc}}=\frac{\sqrt c+\sqrt a}{\sqrt{ac}}.$$

Ответ

а) $$\frac{x+z}{\sqrt{xyz}}$$;
б) $$\frac{m-\sqrt{nr}}{\sqrt{mnr}}$$;
в) $$\frac{m-c}{\sqrt{cdm}}$$;
г) $$\frac{\sqrt c+\sqrt a}{\sqrt{ac}}$$.