1. 6x*a/3x^2 2. 1-2c/c^3-1 - c-1/c^2+c+1 3. 4a/5b:2a^2/15b^2 4. 3/x^2-2x*2x-4/x

1. 6xa/3x^2 = 2a/x;

2. (1 - 2c) / (c^3 - 1) - (c - 1) / (c^2 + c + 1) = (1 - 2c) / ((c - 1) (c^2 + c + 1)) - (c - 1) / (c^2 + c + 1) = (1 - 2c - (c - 1) ^2) / ((c - 1) (c^2 + c + 1)) = (1 - 2c - c^2 + 2c - 1) / ((c - 1) (c^2 + c + 1)) = - c^2 / (c^3 - 1);

3. 4a/5b : 2a^2/15b^2 = 4a/5b * 15b^2/2a^2 = 3b/a;

4. 3 / (x^2 - 2x) * (2x - 4) / x = 3 / (x (x - 2)) * (2 (x - 2)) / x = 6/x^2.