$\frac{3x - 6y}{3x} = \frac{3(x - 2y)}{3x} = \frac{x - 2y}{x}$

$\frac{3a + 9b}{4a + 12b} = \frac{3(a + 3b)}{4(a + 3b)} = \frac{3}{4}$

$\frac{a^2 - 49}{3a + 21} = \frac{(a - 7)(a + 7)}{3(a + 7)} = \frac{a - 7}{3}$

$\frac{12x^2 - 4x}{2 - 6x} = \frac{4x(3x - 1)}{2(1 - 3x)} = -\frac{4x(3x - 1)}{2(3x - 1)} = -2x$

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

$\frac{b^7 + b^4}{b^2 + b^5} = \frac{b^4(b^3 + 1)}{b^2(1 + b^3)} = b^2$

$\frac{a^3 + 64}{3a + 12} = \frac{(a + 4)(a^2 - 4a + 16)}{3(a + 4)} = \frac{a^2 - 4a + 16}{3}$

$\frac{xb - 5y + 5b - xy}{x^2 - 25} = \frac{(xb - xy) + (-5y + 5b)}{(x - 5)(x + 5)} = \frac{x(b - y) + 5(b - y)}{(x - 5)(x + 5)} = \frac{(b - y)(x + 5)}{(x - 5)(x + 5)} = \frac{b - y}{x - 5}$

$\frac{7m^2 - 7m + 7}{14m^3 + 14} = \frac{7(m^2 - m + 1)}{14(m^3 + 1)} = \frac{m^2 - m + 1}{2(m + 1)(m^2 - m + 1)} = \frac{1}{2(m + 1)}$

$\frac{a^2 + bc - b^2 + ac}{ab + c^2 + ac - b^2} = \frac{(a^2 - b^2) + (ac + bc)}{(ab + ac) + (c^2 - b^2)} = \frac{(a - b)(a + b) + c(a + b)}{a(b + c) + (c - b)(c + b)} = \frac{(a + b)(a - b + c)}{(b + c)(a - b + c)} = \frac{a + b}{b + c}$

$\frac{20mn^2 - 20m^2n + 5m^3}{10mn - 5m^2} = \frac{5m(4n^2 - 4mn + m^2)}{5m(2n - m)} = \frac{(2n - m)^2}{2n - m} = 2n - m$

$\frac{x^2 - yz + xz - y^2}{x^2 + yz - xz - y^2} = \frac{(x^2 - y^2) + (xz - yz)}{(x^2 - y^2) + (yz - xz)} = \frac{(x - y)(x + y) + z(x - y)}{(x - y)(x + y) - z(x - y)} = \frac{(x - y)(x + y + z)}{(x - y)(x + y - z)} = \frac{x + y + z}{x + y - z}$