Упр.71 ГДЗ Колягин Ткачёва 9 класс (Алгебра)

1) (x-y)/(x^(1/2)+y^(1/2)); 2) (va-vb)/(a^(1/4)-b^(1/4));
3) (m^(1/2)+n^(1/2))/(m+2v(mn)+n); 4) (c-2c^(1/2)+1)/(vc-1).

1. $$\frac{x-y}{\sqrt{x}+\sqrt{y}}=\frac{(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y})}{\sqrt{x}+\sqrt{y}}=\sqrt{x}-\sqrt{y}.$$

2. $$\frac{\sqrt{a}-\sqrt{b}}{\sqrt[4]{a}-\sqrt[4]{b}}=\frac{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})}{\sqrt[4]{a}-\sqrt[4]{b}}=\sqrt[4]{a}+\sqrt[4]{b}.$$

3. $$\frac{\sqrt{m}+\sqrt{n}}{m+2\sqrt{mn}+n}=\frac{\sqrt{m}+\sqrt{n}}{(\sqrt{m}+\sqrt{n})^2}=\frac{1}{\sqrt{m}+\sqrt{n}}.$$

4. $$\frac{c-2\sqrt{c}+1}{\sqrt{c}-1}=\frac{(\sqrt{c}-1)^2}{\sqrt{c}-1}=\sqrt{c}-1.$$

Ответ

1) $$\sqrt{x}-\sqrt{y}$$; 2) $$\sqrt[4]{a}+\sqrt[4]{b}$$; 3) $$\frac{1}{\sqrt{m}+\sqrt{n}}$$; 4) $$\sqrt{c}-1$$.