Решебник по алгебре 8 класс Мерзляк Задание 745

\[\boxed{\mathbf{745\ (745).\ }Еуроки\ - \ ДЗ\ без\ мороки}\]

\[1)\ \frac{4a - 16}{a^{2} - 16} = \frac{4 \cdot (a - 4)}{(a - 4)(a + 4)} =\]

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

\[2)\ \frac{12b^{3} - 8b^{2}}{2 - 3b} = \frac{4b^{2}(3b - 2)}{(2 - 3b)} =\]

\[= - 4b²\]

\[3)\ \frac{c^{2} + 10c + 25}{5c + 25} = \frac{(c + 5)^{2}}{5 \cdot (c + 5)} =\]

\[= \frac{c + 5}{5}\]

\[4)\ \frac{4 - m^{2}}{m^{2} - 4m + 4} =\]

\[= \frac{(2 - m)(2 + m)}{(m - 2)^{2}} = \frac{- 2 - m}{m - 2} =\]

\[= \frac{2 + m}{2 - m}\]

\[5)\ \frac{n^{3} - n^{5}}{n^{3} - n} = \frac{n^{3}\left( 1 - n^{2} \right)}{n\left( n^{2} - 1 \right)} = - n²\]

\[6)\ \frac{2 - 2x^{2}}{4x^{2} - 8x + 4} = \frac{2 \cdot \left( 1 - x^{2} \right)}{(2x - 2)^{2}} =\]

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

\[= \frac{1 + x}{2 - 2x}\]