Решебник по алгебре и начала математического анализа 10 класс Колягин Задание 11

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\[1)\ \frac{12a^{2}b^{3}c^{5}}{27a^{4}b^{3}c^{2}} = \frac{4c^{3}}{9a^{2}}\]

\[2)\ \frac{a^{7}(a - b)^{2}\ }{a^{4}(a - b)^{3}} = \frac{a^{3}}{a - b}\]

\[3)\ \frac{2a + 6}{a^{2} - 9} = \frac{2 \cdot (a + 3)}{(a - 3)(a + 3)} =\]

\[= \frac{2}{a - 3}\]

\[4)\ \frac{(m - 2n)^{2}}{10n - 5m} = \frac{(2n - m)^{2}}{5 \cdot (2n - m)} =\]

\[= \frac{2n - m}{5}\]

\[5)\ \frac{a^{2} - 4}{a^{3} + 8} =\]

\[= \frac{(a - 2)(a + 2)}{(a + 2)\left( a^{2} - 2a + 4 \right)} =\]

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

\[6)\ \frac{8a^{3} - 27}{9 - 4a^{2}} =\]

\[= \frac{(2a - 3)\left( 4a^{2} + 6a + 9 \right)}{(3 - 2a)(3 + 2a)} =\]

\[= - \frac{4a^{2} + 6a + 9}{2a + 3}\]