Решебник по алгебре 8 класс Мерзляк ФГОС Задание 546

 

\[\boxed{\mathbf{546\ (546).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\frac{a^{2} - 7}{a + \sqrt{7}} = \frac{\left( a - \sqrt{7} \right)\left( a + \sqrt{7} \right)}{\left( a + \sqrt{7} \right)} =\]

\[= a - \sqrt{7}\]

\[2)\ \frac{\sqrt{3} - b}{3 - b^{2}} = \frac{\left( \sqrt{3} - b \right)}{\left( \sqrt{3} - b \right)\left( \sqrt{3} + b \right)} =\]

\[= \frac{1}{\sqrt{3} + b}\]

\[3)\ \frac{c - 9}{\sqrt{c} - 3} = \frac{\left( \sqrt{c} - 3 \right)\left( \sqrt{c} + 3 \right)}{\left( \sqrt{c} - 3 \right)} =\]

\[= \sqrt{c} + 3\]

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

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

\[= \sqrt{a} - \sqrt{b}\]

\[5)\ \frac{5\sqrt{a} - 7\sqrt{b}}{25a - 49b} =\]

\[= \frac{\left( 5\sqrt{a} - 7\sqrt{b} \right)}{\left( 5\sqrt{a} - 7\sqrt{b} \right)\left( 5\sqrt{a} + 7\sqrt{b} \right)} =\]

\[= \frac{1}{5\sqrt{a} + 7\sqrt{b}}\]

\[6)\ \frac{100a^{2} - 9b}{10a + 3\sqrt{b}} =\]

\[= \frac{\left( 10a - 3\sqrt{b} \right)\left( 10a + 3\sqrt{b} \right)}{\left( 10a + 3\sqrt{b} \right)} =\]

\[= 10a - 3\sqrt{b}\]

\[7)\ \frac{\sqrt{2} - 1}{\sqrt{6} - \sqrt{3}} = \frac{\left( \sqrt{2} - 1 \right)}{\sqrt{3} \cdot \left( \sqrt{2} - 1 \right)} =\]

\[= \frac{1}{\sqrt{3}}\]

\[8)\ \frac{\sqrt{35} + \sqrt{10}}{\sqrt{7} + \sqrt{2}} =\]

\[= \frac{\sqrt{5} \cdot \left( \sqrt{7} + \sqrt{2} \right)}{\left( \sqrt{7} + \sqrt{2} \right)} = \sqrt{5}\]

\[9)\ \frac{\sqrt{15} - \sqrt{6}}{5 - \sqrt{10}} =\]

\[= \frac{\sqrt{3} \cdot \left( \sqrt{5} - \sqrt{2} \right)}{\sqrt{5} \cdot \left( \sqrt{5} - \sqrt{2} \right)} = \sqrt{\frac{3}{5}}\]

\[10)\ \frac{13 - \sqrt{13}}{\sqrt{13}} =\]

\[= \frac{\sqrt{13} \cdot \left( \sqrt{13} - 1 \right)}{\sqrt{13}} = \sqrt{13} - 1\]

\[11)\ \frac{a + 2\sqrt{\text{ab}} + b}{\sqrt{a} + \sqrt{b}} =\]

\[= \frac{\left( \sqrt{a} + \sqrt{b} \right)^{2}}{\sqrt{a} + \sqrt{b}} = \sqrt{a} + \sqrt{b}\]

\[12)\ \frac{4b^{2} - 4b\sqrt{c} + c}{2b - \sqrt{c}} =\]

\[= \frac{(2b - \sqrt{c})²}{(2b - \sqrt{c})} = 2b - \sqrt{c}\]

\[\boxed{\mathbf{5}\mathbf{4}\mathbf{6}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{a(a - 5)}{(a - 5)^{2}} + \frac{25}{(a - 5)(a + 5)} =\]

\[= \frac{a}{a - 5} + \frac{25}{(a - 5)(a + 5)} =\]

\[= \frac{a² + 5a + 25}{(a - 5)(a + 5)}\]

\[2)\ \frac{a^{2} + 5a + 25}{(a - 5)(a + 5)}\text{\ \ }:\frac{125 - a^{3}}{5 + a} =\]

\[= - \frac{1}{(a - 5)^{2}}\]

\[при\ a = 4,5 \Longrightarrow - \frac{1}{(4,5 - 5)^{2}} =\]

\[= - \frac{1}{\left( - \frac{1}{2} \right)^{2}} = - 4.\ \]