Упр.17.35 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

Задача

1) ((va-vb)/(a+vab)-1/(a-b)•(vb-va)^2/(va+vb)) :(va-vb)/(a+vab);
2) (va+vb-(2vab)/(va+vb)) :((va-vb)/(va+vb)+vb/va);
3) ((va+1)/(vab+1)+(vab+va)/(vab-1)-1) :((va+1)/(vab+1)-(vab+va)/(vab-1)+1);
4) (ava+bvb)/(va+vb) :(a-b)+(2vb)/(va+vb);
5) (1/(va-v(a-b))+1/(va+v(a+b))) :(1+v((a+b)/(a-b)));
6) ((v(a/b)-v(b/a)) :(v(a/b)+v(b/a)-2)) :(1+v(b/a)),a > 0,b > 0.

Подробный ответ

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