2. Упростите выражение: 1) 3x x-4 - x+3 * 2x-8 x+3 x²+3x² 96 ; 2) x+3 x-4 : x-3 x+3 ; 9-x² 6x

1)

$$\frac{3x}{x-4} - \frac{x+3}{x+3} \cdot \frac{2x-8}{x^2+3x^2} \cdot \frac{96}{1} = \frac{3x}{x-4} - 1 \cdot \frac{2(x-4)}{4x^2} \cdot 96 = \frac{3x}{x-4} - \frac{2(x-4) \cdot 96}{4x^2} = \frac{3x}{x-4} - \frac{192(x-4)}{4x^2} = \frac{3x}{x-4} - \frac{48(x-4)}{x^2} = \frac{3x^3 - 48(x-4)^2}{x^2(x-4)} = \frac{3x^3 - 48(x^2-8x+16)}{x^2(x-4)} = \frac{3x^3 - 48x^2+384x-768}{x^2(x-4)}$$

Ответ: $$\frac{3x^3 - 48x^2+384x-768}{x^2(x-4)}$$

2)

$$(\frac{x+3}{x-4} : \frac{x-3}{x+3}) : \frac{9-x^2}{6x} = (\frac{x+3}{x-4} \cdot \frac{x+3}{x-3}) : \frac{9-x^2}{6x} = \frac{(x+3)^2}{(x-4)(x-3)} \cdot \frac{6x}{9-x^2} = \frac{(x+3)^2}{(x-4)(x-3)} \cdot \frac{6x}{(3-x)(3+x)} = \frac{(x+3)^2}{(x-4)(x-3)} \cdot \frac{6x}{-(x-3)(x+3)} = \frac{(x+3) \cdot 6x}{-(x-4)(x-3)^2} $$

Ответ: $$\frac{(x+3) \cdot 6x}{-(x-4)(x-3)^2} $$