$\frac{5m-2n}{10k}:\frac{5m-2n}{10k^2}=\frac{5m-2n}{10k}\ast \frac{10k^2}{5m-2n}=\frac{1}{1}\ast \frac{k}{1}=k$

$\frac{p+3}{p^2-2p}:\frac{p+3}{4p-8}=\frac{p+3}{p(p-2)}:\frac{p+3}{4(p-2)}=\frac{p+3}{p(p-2)}\ast \frac{4(p-2)}{p+3}=\frac{1}{p}\ast \frac{4}{1}=\frac{4}{p}$

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

$\frac{a^2-16}{a-3}:\frac{a+4}{a-3}=\frac{(a-4)(a+4)}{a-3}:\frac{a+4}{a-3}=\frac{(a-4)(a+4)}{a-3}\ast \frac{a-3}{a+4}=\frac{a-4}{1}\ast \frac{1}{1}=a-4$

$\frac{y-9}{y-8}:\frac{y^2-81}{y^2-16y+64}=\frac{y-9}{y-8}:\frac{(y-9)(y+9)}{(y-8{)}^2}=\frac{y-9}{y-8}\ast \frac{(y-8{)}^2}{(y-9)(y+9)}=\frac{1}{1}\ast \frac{y-8}{y+9}=\frac{y-8}{y+9}$

$(x^2-49y^2):\frac{x-7y}{x}=(x-7y)(x+7y):\frac{x-7y}{x}=(x-7y)(x+7y)\ast \frac{x}{x-7y}=(x+7y)\ast \frac{x}{1}=x(x+7y)$