$\frac{a - b}{7a} : \frac{a - b}{7b} = \frac{a - b}{7a} * \frac{7b}{a - b} = \frac{1}{a} * \frac{b}{1} = \frac{b}{a}$

$\frac{x^2 - y^2}{x^2} : \frac{6x + 6y}{x^5} = \frac{(x - y)(x + y)}{x^2} : \frac{6(x + y)}{x^5} = \frac{(x - y)(x + y)}{x^2} * \frac{x^5}{6(x + y)} = \frac{x - y}{1} * \frac{x^3}{6} = \frac{x^3(x - y)}{6}$

$\frac{c - 5}{c^2 - 4c} : \frac{c - 5}{5c - 20} = \frac{c - 5}{c(c - 4)} : \frac{c - 5}{5(c - 4)} = \frac{c - 5}{c(c - 4)} * \frac{5(c - 4)}{c - 5} = \frac{1}{c} * \frac{5}{1} = \frac{5}{c}$

$\frac{x - y}{xy} : \frac{x^2 - y^2}{3xy} = \frac{x - y}{xy} : \frac{(x - y)(x + y)}{3xy} = \frac{x - y}{xy} * \frac{3xy}{(x - y)(x + y)} = \frac{1}{1} * \frac{3}{x + y} = \frac{3}{x + y}$

$\frac{a^2 - 25}{a + 7} : \frac{a - 5}{a + 7} = \frac{(a - 5)(a + 5)}{a + 7} : \frac{a - 5}{a + 7} = \frac{(a - 5)(a + 5)}{a + 7} * \frac{a + 7}{a - 5} = \frac{a + 5}{1} * \frac{1}{1} = a + 5$

$\frac{a^2 - 4a + 4}{a + 2} : (a - 2) = \frac{(a - 2)^2}{a + 2} : (a - 2) = \frac{(a - 2)^2}{a + 2} * \frac{1}{a - 2} = \frac{a - 2}{a + 2} * \frac{1}{1} = \frac{a - 2}{a + 2}$

$(p^2 - 16k^2) : \frac{p + 4k}{p} = (p - 4k)(p + 4k) : \frac{p + 4k}{p} = (p - 4k)(p + 4k) * \frac{p}{p + 4k} = (p - 4k) * \frac{p}{1} = p(p - 4k)$

$\frac{a^2 - ab}{a^2} : \frac{a^2 - 2ab + b^2}{ab} = \frac{a(a - b)}{a^2} : \frac{(a - b)^2}{ab} = \frac{a(a - b)}{a^2} * \frac{ab}{(a - b)^2} = \frac{a - b}{a} * \frac{ab}{(a - b)^2} = \frac{1}{1} * \frac{b}{a - b} = \frac{b}{a - b}$