Сократите дробь: A) \(\frac{4x + 8}{3x^2 + 5x - 2}\); Б) \(\frac{3x^2 - 12}{3x^2 - 7x + 2}\); B) \(\frac{2x^2 + 5x + 2}{8 - 2x^2}\); Г) \(\frac{42 - x - x^2}{2x^2 - 13x + 6}\);

Решение:

1. A) \(\frac{4x + 8}{3x^2 + 5x - 2}\) = \(\frac{4(x + 2)}{3x^2 + 6x - x - 2}\) = \(\frac{4(x + 2)}{3x(x + 2) - 1(x + 2)}\) = \(\frac{4(x + 2)}{(3x - 1)(x + 2)}\) = \(\frac{4}{3x - 1}\)
2. Б) \(\frac{3x^2 - 12}{3x^2 - 7x + 2}\) = \(\frac{3(x^2 - 4)}{3x^2 - x - 6x + 2}\) = \(\frac{3(x - 2)(x + 2)}{x(3x - 1) - 2(3x - 1)}\) = \(\frac{3(x - 2)(x + 2)}{(x - 2)(3x - 1)}\) = \(\frac{3(x + 2)}{3x - 1}\)
3. B) \(\frac{2x^2 + 5x + 2}{8 - 2x^2}\) = \(\frac{2x^2 + 4x + x + 2}{8 - 2x^2}\) = \(\frac{2x(x + 2) + 1(x + 2)}{2(4 - x^2)}\) = \(\frac{(2x + 1)(x + 2)}{2(2 - x)(2 + x)}\) = \(\frac{2x + 1}{2(2 - x)}\) = -\(\frac{2x + 1}{2(x - 2)}\) = -\(\frac{2x + 1}{2x - 4}\)
4. Г) \(\frac{42 - x - x^2}{2x^2 - 13x + 6}\) = \(\frac{-x^2 - x + 42}{2x^2 - 13x + 6}\) = \(\frac{-(x^2 + x - 42)}{2x^2 - x - 12x + 6}\) = \(\frac{-(x - 6)(x + 7)}{x(2x - 1) - 6(2x - 1)}\) = \(\frac{-(x - 6)(x + 7)}{(x - 6)(2x - 1)}\) = -\(\frac{x + 7}{2x - 1}\) = -\(\frac{x + 7}{2x - 1}\)

Ответ: A) \(\frac{4}{3x - 1}\); Б) \(\frac{3(x + 2)}{3x - 1}\); B) -\(\frac{2x + 1}{2x - 4}\); Г) -\(\frac{x + 7}{2x - 1}\)