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

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

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

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

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

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

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

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