Question

Задание на фото!!!! Заранее спасибо!​

Answer 1

а) $\dfrac{x^{3} - 3x^{2} + 2x - 6}{x^{3} - 27} = \dfrac{x^{2}(x - 3) + 2(x - 3)}{(x - 3)(x^{2} + 3x + 9)} = \dfrac{(x - 3)(x^{2} + 2)}{(x - 3)(x^{2} + 3x + 9)} =$

$= \dfrac{x^{2} + 2}{x^{2} + 3x + 9}$

б) $\dfrac{18a^{2}c - 8b^{2}c^{3}}{6ac - 4bc^{2}} = \dfrac{2c(9a^{2} - 4b^{2}c^{2})}{2c(3a - 2bc)} = \dfrac{(3a-2bc)(3a + 2bc)}{3a - 2bc} = 3a + 2bc$

в) $\dfrac{(3a^{2} - 48)(2a + 8)}{6a^{2} + 48a + 96} = \dfrac{3(a^{2} - 16) \cdot 2(a + 4)}{6(a^{2} + 8a + 16)} = \dfrac{(a - 4)(a + 4) \cdot (a + 4)}{(a + 4)^{2}} = a - 4$