Упр.16.68 ГДЗ Мордкович 8 класс (Алгебра)

Упростите выражение:

а)

$$\frac{\sqrt{x}-\sqrt{y}}{5}-\frac{\sqrt{x}}{5} = \frac{\sqrt{x}-\sqrt{y}-\sqrt{x}}{5} = -\frac{\sqrt{y}}{5}$$

б)

$$\frac{11\sqrt{x}-2\sqrt{y}}{4\sqrt{x}}+\frac{2\sqrt{x}-3\sqrt{y}}{4\sqrt{x}}-\frac{\sqrt{x}-\sqrt{y}}{4\sqrt{x}} = \frac{11\sqrt{x}-2\sqrt{y}+2\sqrt{x}-3\sqrt{y}-\sqrt{x}+\sqrt{y}}{4\sqrt{x}}$$
$$= \frac{12\sqrt{x}-4\sqrt{y}}{4\sqrt{x}} = \frac{4(3\sqrt{x}-\sqrt{y})}{4\sqrt{x}} = \frac{3\sqrt{x}-\sqrt{y}}{\sqrt{x}}$$

в)

$$\frac{\sqrt{m}}{12}-\frac{\sqrt{m}+\sqrt{n}}{12} = \frac{\sqrt{m}-\sqrt{m}-\sqrt{n}}{12} = -\frac{\sqrt{n}}{12}$$

г)

$$\frac{2\sqrt{c}-\sqrt{d}}{5\sqrt{c}}-\frac{8\sqrt{c}+6\sqrt{d}}{5\sqrt{c}}+\frac{\sqrt{c}-3\sqrt{d}}{5\sqrt{c}} = \frac{2\sqrt{c}-\sqrt{d}-8\sqrt{c}-6\sqrt{d}+\sqrt{c}-3\sqrt{d}}{5\sqrt{c}}$$
$$= \frac{-5\sqrt{c}-10\sqrt{d}}{5\sqrt{c}} = \frac{-5(\sqrt{c}+2\sqrt{d})}{5\sqrt{c}} = -\frac{\sqrt{c}+2\sqrt{d}}{\sqrt{c}}$$

Ответ

а) $$-\frac{\sqrt{y}}{5}$$; б) $$\frac{3\sqrt{x}-\sqrt{y}}{\sqrt{x}}$$; в) $$-\frac{\sqrt{n}}{12}$$; г) $$-\frac{\sqrt{c}+2\sqrt{d}}{\sqrt{c}}$$