Решебник по алгебре 8 класс Мерзляк ФГОС Задание 862

 

\[\boxed{\mathbf{862\ (862).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{x^{2} - 10x + 25}{x^{2} - 100}\ :\frac{x - 5}{x - 10} =\]

\[= \frac{(x - 5)^{2}(x - 10)}{(x - 10)(x + 10)(x - 5)} =\]

\[= \frac{x - 5}{x + 10}\]

\[2)\ \frac{a^{2} - 1}{a - 8}\ :\frac{a^{2} + 2a + 1}{a - 8} =\]

\[= \frac{(a - 1)(a + 1)(a - 8)}{(a - 8)(a + 1)^{2}} =\]

\[= \frac{a - 1}{a + 1}\]

\[3)\ \frac{ab + b^{2}}{8b}\ :\frac{ab + a^{2}}{2a} =\]

\[= \frac{b(a + b) \cdot 2a}{8b \cdot a(b + a)} = \frac{1}{4}\]

\[4)\ \frac{2c - 3}{c - 1}\ :(2c - 3) =\]

\[= \frac{2c - 3}{(2c - 3)(c - 1)} = \frac{1}{c - 1}\]

\[= \frac{(x - 4y)(5x + 2y)}{(x + 4y)(5x - 2y)}\]

\[6)\ \frac{n^{2} - 3n}{49n^{2} - 1}\ :\frac{n^{4} - 27n}{49n^{2} - 14n + 1} =\]

\[= \frac{7n - 1}{(7n + 1)(n^{2} + 3n + 9)}\]

\[= \frac{a(3a^{2} - b^{2})}{6 \cdot (a - 4b)}\]

\[\boxed{\mathbf{8}\mathbf{6}\mathbf{2}\mathbf{\text{.\ }}Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ ab > 0\]

\[a > 0;\ \ b > 0\ или\]

\[a < 0;\ \ b < 0.\]

\[2)\ \ ab < 0\]

\[a < 0;b > 0\ или\]

\[a > 0;\ \ b < 0.\]

\[3)\ \frac{a}{b} > 0\]

\[a > 0;\ \ b > 0\ \ или\]

\[a < 0;\ \ b < 0.\]

\[4)\ \frac{a}{b} < 0\]

\[a < 0;\ \ b > 0\ или\]

\[a > 0;\ \ b < 0.\]

\[5)\ \ a^{2}b > 0\]

\[a - любое\ число \neq 0;b > 0.\]

\[6)\ a^{2}b < 0\]

\[a - любое\ число \neq 0;b < 0.\]