Решебник по алгебре 8 класс Мерзляк Задание 185

\[\boxed{\text{185\ (185).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]

\[1)\frac{3x^{2} - 27}{4x^{2} + 2} \cdot\]

\[\cdot \left( \frac{6x + 1^{\backslash x + 3}}{x - 3} + \frac{6x - 1^{\backslash x - 3}}{x + 3} \right) =\]

\[= \frac{3x^{2} - 27}{4x^{2} + 2} \cdot\]

\[\cdot \left( \frac{6x^{2} + x + 18x + 3 + 6x^{2} - x - 18x + 3}{(x - 3)(x + 3)} \right) =\]

\[= \frac{3 \cdot \left( x^{2} - 9 \right)}{2 \cdot \left( 2x^{2} + 1 \right)} \cdot \frac{12x^{2} + 6}{(x - 3)(x + 3)} =\]

\[= \frac{3(x - 3)(x + 3) \cdot 6 \cdot \left( 2x^{2} + 1 \right)}{2\left( 2x^{2} + 1 \right)(x - 3)(x + 3)} =\]

\[= \frac{18}{2} = 9\]

\[2)\ \frac{3}{2a - 3} - \frac{8a^{3} - 18a}{4a^{2} + 9} \cdot\]

\[\cdot \left( \frac{2a}{4a^{2} - 12a + 9} - \frac{3}{4a^{2} - 9} \right) =\]

\[= \frac{3}{2a - 3} - \frac{8a^{3} - 18a}{4a^{2} + 9} \cdot\]

\[\cdot \left( \frac{2a^{\backslash 2a + 3}}{(2a - 3)^{2}} - \frac{3^{\backslash 2a - 3}}{(2a - 3)(2a + 3)} \right) =\]

\[= \frac{3}{2a - 3} - \frac{8a^{3} - 18a}{4a^{2} + 9} \cdot\]

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

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

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

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

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

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

\[= - 1\]