Упр.17.35 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1. $$\left(\frac{\sqrt a-\sqrt b}{a+\sqrt{ab}}-\frac1{a-b}\cdot\frac{(\sqrt b-\sqrt a)^2}{\sqrt a+\sqrt b}\right):\frac{\sqrt a-\sqrt b}{a+\sqrt{ab}}$$

   $$\left(\frac{\sqrt a-\sqrt b}{\sqrt a(\sqrt a+\sqrt b)}-\frac1{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}\cdot\frac{(\sqrt a-\sqrt b)^2}{\sqrt a+\sqrt b}\right)\cdot\frac{a+\sqrt{ab}}{\sqrt a-\sqrt b}$$

   $$\left(\frac{\sqrt a-\sqrt b}{\sqrt a(\sqrt a+\sqrt b)}-\frac{\sqrt a-\sqrt b}{(\sqrt a+\sqrt b)^2}\right)\cdot\frac{\sqrt a(\sqrt a+\sqrt b)}{\sqrt a-\sqrt b}$$

   $$\frac{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)-\sqrt a(\sqrt a-\sqrt b)}{(\sqrt a+\sqrt b)^2}\cdot\frac{\sqrt a(\sqrt a+\sqrt b)}{\sqrt a-\sqrt b}$$

   $$\frac{a-b-a+\sqrt{ab}}{\sqrt a+\sqrt b}\cdot\frac1{\sqrt a-\sqrt b} =\frac{\sqrt{ab}-b}{(\sqrt a+\sqrt b)(\sqrt a-\sqrt b)}$$

   $$\frac{\sqrt b(\sqrt a-\sqrt b)}{(\sqrt a+\sqrt b)(\sqrt a-\sqrt b)}=\frac{\sqrt b}{\sqrt a+\sqrt b}$$

2. $$\left(\sqrt a+\sqrt b-\frac{2\sqrt{ab}}{\sqrt a+\sqrt b}\right):\left(\frac{\sqrt a-\sqrt b}{\sqrt a+\sqrt b}+\frac{\sqrt b}{\sqrt a}\right)$$

   $$\frac{(\sqrt a+\sqrt b)^2-2\sqrt{ab}}{\sqrt a+\sqrt b}:\frac{\sqrt a(\sqrt a-\sqrt b)+\sqrt b(\sqrt a+\sqrt b)}{\sqrt a(\sqrt a+\sqrt b)}$$

   $$\frac{a+2\sqrt{ab}+b-2\sqrt{ab}}{\sqrt a+\sqrt b}:\frac{a-\sqrt{ab}+\sqrt{ab}+b}{\sqrt a(\sqrt a+\sqrt b)}$$

   $$\frac{a+b}{\sqrt a+\sqrt b}:\frac{a+b}{\sqrt a(\sqrt a+\sqrt b)}=\sqrt a$$

3. $$\left(\frac{\sqrt a+1}{\sqrt{ab}+1}+\frac{\sqrt{ab}+\sqrt a}{\sqrt{ab}-1}-1\right):\left(\frac{\sqrt a+1}{\sqrt{ab}+1}-\frac{\sqrt{ab}+\sqrt a}{\sqrt{ab}-1}+1\right)$$

   $$\frac{(\sqrt a+1)(\sqrt{ab}-1)+(\sqrt{ab}+\sqrt a)(\sqrt{ab}+1)-(\sqrt{ab}+1)(\sqrt{ab}-1)}{(\sqrt{ab}+1)(\sqrt{ab}-1)}$$

   $$:\frac{(\sqrt a+1)(\sqrt{ab}-1)-(\sqrt{ab}+\sqrt a)(\sqrt{ab}+1)+(\sqrt{ab}+1)(\sqrt{ab}-1)}{(\sqrt{ab}+1)(\sqrt{ab}-1)}$$

   $$\frac{2\sqrt{ab}(\sqrt a+1)}{ab-1}:\frac{-2(\sqrt a+1)}{ab-1}=-\sqrt{ab}$$

4. $$\frac{a\sqrt a+b\sqrt b}{\sqrt a+\sqrt b}:(a-b)+\frac{2\sqrt b}{\sqrt a+\sqrt b}$$

   $$\frac{a\sqrt a+b\sqrt b}{(\sqrt a+\sqrt b)(a-b)}+\frac{2\sqrt b}{\sqrt a+\sqrt b}$$

   $$\frac{a-\sqrt{ab}+b}{a-b}+\frac{2\sqrt b(\sqrt a-\sqrt b)}{a-b} =\frac{a+\sqrt{ab}-b}{a-b}$$

5. $$\left(\frac1{\sqrt a-\sqrt{a-b}}+\frac1{\sqrt a+\sqrt{a+b}}\right):\left(1+\sqrt{\frac{a+b}{a-b}}\right)$$

   $$\left(\frac{\sqrt a+\sqrt{a-b}}{b}+\frac{\sqrt a-\sqrt{a+b}}{-b}\right):\frac{\sqrt{a-b}+\sqrt{a+b}}{\sqrt{a-b}}$$

   $$\frac{\sqrt{a-b}+\sqrt{a+b}}{b}\cdot\frac{\sqrt{a-b}}{\sqrt{a-b}+\sqrt{a+b}}=\frac{\sqrt{a-b}}{b}$$

6. $$\left(\left(\sqrt{\frac ab}-\sqrt{\frac ba}\right):\left(\sqrt{\frac ab}+\sqrt{\frac ba}-2\right)\right):\left(1+\sqrt{\frac ba}\right)$$

   $$\left(\frac{\sqrt a}{\sqrt b}-\frac{\sqrt b}{\sqrt a}\right):\left(\frac{\sqrt a}{\sqrt b}+\frac{\sqrt b}{\sqrt a}-2\right):\left(1+\frac{\sqrt b}{\sqrt a}\right)$$

   $$\left(\frac{a-b}{\sqrt{ab}}:\frac{a+b-2\sqrt{ab}}{\sqrt{ab}}\right):\frac{\sqrt a+\sqrt b}{\sqrt a}$$

   $$\frac{(\sqrt a-\sqrt b)(\sqrt a+\sqrt b)}{(\sqrt a-\sqrt b)^2}\cdot\frac{\sqrt a}{\sqrt a+\sqrt b} =\frac{\sqrt a}{\sqrt a-\sqrt b}$$

Ответ

1. $$\frac{\sqrt b}{\sqrt a+\sqrt b}$$
2. $$\sqrt a$$
3. $$-\sqrt{ab}$$
4. $$\frac{a+\sqrt{ab}-b}{a-b}$$
5. $$\frac{\sqrt{a-b}}{b}$$
6. $$\frac{\sqrt a}{\sqrt a-\sqrt b}$$