$\frac{14a^3}{21a}=\frac{7a\ast <!--\; \ast \; -->2a^2}{7a\ast <!--\; \ast \; -->3}=\frac{2a^2}{3}$

$\frac{8b^3{c}^2}{12b{c}^3}=\frac{4b{c}^2\ast <!--\; \ast \; -->2b^2}{4b{c}^2\ast <!--\; \ast \; -->3c}=\frac{2b^2}{3c}$

$\frac{5x}{20x}=\frac{5x\ast <!--\; \ast \; -->1}{5x\ast <!--\; \ast \; -->4}=\frac{1}{4}$

$\frac{24x^2{y}^2}{32xy}=\frac{8xy\ast <!--\; \ast \; -->3xy}{8xy\ast <!--\; \ast \; -->4}=\frac{3xy}{4}$

$\frac{4abc}{16a{b}^4}=\frac{4ab\ast <!--\; \ast \; -->c}{4ab\ast <!--\; \ast \; -->4b^3}=\frac{c}{4b^3}$

$\frac{56m^5{n}^7}{42m^5{n}^{10}}=\frac{2m^5{n}^7\ast <!--\; \ast \; -->28}{2m^5{n}^7\ast <!--\; \ast \; -->21n^3}=\frac{28}{21n^3}$

$\frac{-<!--\; -\; -->10n^{10}}{5n^4}=-<!--\; -\; -->\frac{5n^4\ast <!--\; \ast \; -->2n^6}{5n^4\ast <!--\; \ast \; -->1}=-<!--\; -\; -->2n^6$

$\frac{3p^4{q}^6}{-<!--\; -\; -->9p^8{q}^7}=-<!--\; -\; -->\frac{3p^4{q}^6\ast <!--\; \ast \; -->1}{3p^4{q}^6\ast <!--\; \ast \; -->3p^{4}q}=-<!--\; -\; -->\frac{1}{3p^{4}q}$