Упр.16.76 ГДЗ Мордкович 8 класс (Алгебра)

15.76

1. а)

   $$\frac{\sqrt a}{x-3\sqrt x}:\frac{\sqrt a}{3\sqrt x-9}= \frac{\sqrt a}{x-3\sqrt x}\cdot\frac{3\sqrt x-9}{\sqrt a}$$
   $$=\frac{3(\sqrt x-3)}{\sqrt x(\sqrt x-3)}=\frac{3}{\sqrt x}.$$

2. б)

   $$\frac{\sqrt a+a}{\sqrt n}\cdot\frac{n}{3+3\sqrt a}= \frac{\sqrt a(1+\sqrt a)}{\sqrt n}\cdot\frac{n}{3(1+\sqrt a)}$$
   $$=\frac{\sqrt a\cdot n}{3\sqrt n}=\frac{\sqrt{an}}{3}.$$

3. в)

   $$\frac{\sqrt{rx}+r}{x}:\frac{\sqrt x+\sqrt r}{\sqrt x}= \frac{\sqrt r(\sqrt x+\sqrt r)}{x}\cdot\frac{\sqrt x}{\sqrt x+\sqrt r}$$
   $$=\frac{\sqrt r\cdot\sqrt x}{x}=\frac{\sqrt r}{\sqrt x}.$$

4. г)

   $$\frac{6\sqrt n}{n-\sqrt n}:\frac{3\sqrt{an}}{2\sqrt n-2}= \frac{6\sqrt n}{\sqrt n(\sqrt n-1)}\cdot\frac{2(\sqrt n-1)}{3\sqrt{an}}$$
   $$=\frac{4}{\sqrt{an}}.$$

Ответ

а) $$\frac{3}{\sqrt x}$$; б) $$\frac{\sqrt{an}}{3}$$; в) $$\frac{\sqrt r}{\sqrt x}$$; г) $$\frac{4}{\sqrt{an}}$$.