Сократите дробь (26-41):

Решение:

1. \((3x^2 - 7x + 2) / (2x - 3x^2)\) = \((3x-1)(x-2) / (x(2-3x))\) = \(-(3x-1)(x-2) / (x(3x-2))\)
2. \((5x^2 - 12x + 4) / (6 - 15x)\) = \((5x-2)(x-2) / (3(2-5x))\) = \(-(5x-2)(x-2) / (3(5x-2))\) = \(-(x-2) / 3\)
3. \((2 - 6x) / (x - 7x^2)\) = \(2(1-3x) / (x(1-7x))\) (не сокращается)
4. \((16a^2 - 8a + 1) / (1 - 4a + x - 4ax)\) = \((4a-1)^2 / (1-4a) + x(1-4a)\) = \((4a-1)^2 / ((1-4a)(1+x))\) = \(-(1-4a)^2 / ((1-4a)(1+x))\) = \(-(1-4a) / (1+x)\) = \((4a-1) / (1+x)\)
5. \((6c - 1 - y + 6cy) / (1 - 12c + 36c^2)\) = \((6c(1+y) - (1+y)) / (1-6c)^2\) = \(((6c-1)(1+y)) / (1-6c)^2\) = \(-(1-6c)(1+y) / (1-6c)^2\) = \(-(1+y) / (1-6c)\) = \((1+y) / (6c-1)\)