$\frac{3a+b}{4c}\ast \frac{c}{3a+b}=\frac{1}{4}\ast \frac{1}{1}=\frac{1}{4}$

$\frac{ab-b^2}{8}\ast \frac{4a}{b^4}=\frac{b(a-b)}{8}\ast \frac{4a}{b^4}=\frac{a-b}{2}\ast \frac{a}{b^3}=\frac{a(a-b)}{2b^3}$

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

$\frac{18b}{b^2-16}\ast \frac{b+4}{3b}=\frac{18b}{(b-4)(b+4)}\ast \frac{b+4}{3b}=\frac{6}{b-4}\ast \frac{1}{1}=\frac{6}{b-4}$

$\frac{6}{m^2-9n^2}\ast (m-3n)=\frac{6}{(m-3n)(m+3n)}\ast (m-3n)=\frac{6}{m+3n}\ast 1=\frac{6}{m+3n}$

$\frac{3c-9}{9c^2+6c+1}\ast \frac{3c+1}{c-3}=\frac{3(c-3)}{(3c+1{)}^2}\ast \frac{3c+1}{c-3}=\frac{3}{3c+1}\ast \frac{1}{1}=\frac{3}{3c+1}$