Решебник по алгебре 8 класс Мерзляк ФГОС Задание 588

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

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

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

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

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

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

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

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

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

\[4)\ \frac{\sqrt{c} - 5}{\sqrt{c}}\ :\frac{c - 25}{3c} =\]

\[= \frac{\left( \sqrt{c} - 5 \right) \cdot 3c}{\sqrt{c}(c - 25)} =\]

\[= \frac{3\sqrt{c}\left( \sqrt{c} - 5 \right)}{\left( \sqrt{c} - 5 \right)\left( \sqrt{c} + 5 \right)} = \frac{3\sqrt{c}}{\sqrt{c} + 5}\]