Решебник по алгебре 8 класс Мерзляк Задание 562

\[\boxed{\mathbf{562\ (562).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{\sqrt{a} - 3}{\sqrt{a} + 1} - \frac{\sqrt{a} - 4}{\sqrt{a}} =\]

\[= \frac{a - 3\sqrt{a} - a + 3\sqrt{a} + 4}{\sqrt{a} \cdot \left( \sqrt{a} + 1 \right)} =\]

\[= \frac{4}{a + \sqrt{a}}\]

\[2)\ \frac{\sqrt{a} + 1}{a - \sqrt{\text{ab}}} - \frac{\sqrt{b} + 1}{\sqrt{\text{ab}} - b} =\]

\[= \frac{2\sqrt{\text{ab}} - b - a}{a\sqrt{\text{ab}} - ab - ab + b\sqrt{\text{ab}}} =\]

\[= \frac{\left( - 2\sqrt{\text{ab}} + b + a \right)}{\sqrt{\text{ab}} \cdot \left( - 2\sqrt{\text{ab}} + b + a \right)} =\]

\[= - \frac{1}{\sqrt{\text{ab}}}\]

\[3)\ \frac{\sqrt{x}}{y - 2\sqrt{y}}\ :\frac{\sqrt{x}}{3\sqrt{y} - 6} =\]

\[= \frac{\sqrt{x} \cdot 3 \cdot \left( \sqrt{y} - 2 \right)}{\sqrt{y} \cdot \left( \sqrt{y} - 2 \right) \cdot \sqrt{x}} = \frac{3}{\sqrt{y}}\]

\[= \frac{\sqrt{m}}{\sqrt{m} - \sqrt{n}}\ :\frac{m - n + n}{\sqrt{n} \cdot \left( \sqrt{m} - \sqrt{n} \right)} =\]

\[= \frac{\sqrt{m} \cdot \sqrt{n} \cdot (\sqrt{m} - \sqrt{n})}{\left( \sqrt{m} - \sqrt{n} \right) \cdot m} = \frac{\sqrt{n}}{\sqrt{m}}\]

\[5)\ \left( \frac{\sqrt{x} + 1}{\sqrt{x} - 1} - \frac{4\sqrt{x}}{x - 1} \right) \cdot \frac{x + \sqrt{x}}{\sqrt{x} - 1} =\]

\[= \frac{x + 2\sqrt{x} + 1 - 4\sqrt{x}}{\left( \sqrt{x} - 1 \right)\left( \sqrt{x} + 1 \right)} \cdot \frac{x + \sqrt{x}}{\sqrt{x} - 1} =\]

\[= \frac{\left( \sqrt{x} - 1 \right)^{2} \cdot \sqrt{x} \cdot \left( \sqrt{x} + 1 \right)}{\left( \sqrt{x} - 1 \right)^{2} \cdot \left( \sqrt{x} + 1 \right)} =\]

\[= \sqrt{x}\ \]

\[6)\ \frac{a - 64}{\sqrt{a} + 3} \cdot \frac{1}{a + 8\sqrt{a}} - \frac{\sqrt{a} + 8}{a - 3\sqrt{a}} =\]

\[= \frac{- 22\sqrt{a}}{\sqrt{a} \cdot (a - 9)} = - \frac{22}{a - 9} =\]

\[= \frac{22}{9 - a}\]