Алгебра
Английский
Биология
География
Геометрия
История
Русский
Обществознание
Физика
Химия
Информатика
Литература
МатематикаРешебник по алгебре 8 класс Мерзляк ФГОС Задание 568
Задание 568
\[\boxed{\mathbf{568\ (568).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\ \frac{\left( \sqrt{b} - \sqrt{a} \right)^{2}}{(a - b)\left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{\left( \sqrt{b} - \sqrt{a} \right)^{2}}{\left( \sqrt{a} - \sqrt{b} \right)\left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{- \sqrt{b} + \sqrt{a}}{\left( \sqrt{a} + \sqrt{b} \right)^{2}}\]
\[2)\frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{\text{ab}}} - \frac{\sqrt{a} - \sqrt{b}}{\left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{a - b - a + \sqrt{\text{ab}}}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}} =\]
\[= \frac{\sqrt{\text{ab}} - b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}}\ \]
\[3)\ \frac{\sqrt{\text{ab}} - b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)^{2}}\ :\frac{\sqrt{a} - \sqrt{b}}{a + \sqrt{\text{ab}}} =\]
\[= \frac{\sqrt{b}}{\sqrt{a} + \sqrt{b}}\]
\[1)\ \sqrt{a} + \sqrt{b} - \frac{2\sqrt{\text{ab}}}{\sqrt{a} + \sqrt{b}} =\]
\[= \frac{a + \sqrt{\text{ab}} + \sqrt{\text{ab}} + b - 2\sqrt{\text{ab}}}{\sqrt{a} + \sqrt{b}} =\]
\[= \frac{a + b}{\sqrt{a} + \sqrt{b}}\]
\[2)\ \frac{\sqrt{a} - \sqrt{b}}{\sqrt{a} + \sqrt{b}} + \frac{\sqrt{b}}{\sqrt{a}} =\]
\[= \frac{a - \sqrt{\text{ab}} + \sqrt{\text{ab}} + b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)} =\]
\[= \frac{a + b}{\sqrt{a} \cdot \left( \sqrt{a} + \sqrt{b} \right)}\]
\[3)\frac{(a + b) \cdot \sqrt{a} \cdot (\sqrt{a} + \sqrt{b})}{(\sqrt{a} + \sqrt{b})(a + b)} = \sqrt{a}\ \]
\[\boxed{\mathbf{5}\mathbf{6}\mathbf{8}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]
\[1)\frac{4}{\sqrt{2}} = \frac{4\sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{4\sqrt{2}}{2} = 2\sqrt{2};\]
\[2)\frac{12}{\sqrt{6}} = \frac{12\sqrt{6}}{\sqrt{6} \cdot \sqrt{6}} = \frac{12\sqrt{6}}{6} = 2\sqrt{6};\]
\[3)\frac{18}{\sqrt{5}} = \frac{18\sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{18\sqrt{5}}{5};\]
\[4)\frac{m}{\sqrt{n}} = \frac{m\sqrt{n}}{\sqrt{n} \cdot \sqrt{n}} = \frac{m\sqrt{n}}{n};\]
\[5)\frac{a}{b\sqrt{b}} = \frac{a\sqrt{b}}{b \cdot \sqrt{b} \cdot \sqrt{b}} = \frac{a\sqrt{b}}{b^{2}};\ \]
\[6)\frac{5}{\sqrt{15}} = \frac{5\sqrt{15}}{15} = \frac{\sqrt{15}}{3};\]
\[7)\frac{7}{\sqrt{7}} = \frac{7\sqrt{7}}{7} = \sqrt{7};\]
\[8)\frac{24}{5\sqrt{3}} = \frac{24\sqrt{3}}{15} = \frac{8\sqrt{3}}{5}.\]
