Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\frac{6}{25}$
$\frac{15\times4xy\times9}{6\times25x\times15y}\longrightarrow$ Use prime factorization. $\frac{3\times5\times2\times2\times xy\times3\times3}{2\times3\times5\times5\times x\times3\times5\times y}\longrightarrow$ Reorder $\frac{2\times2\times3\times3\times3\times5\times x\times y}{2\times3\times3\times5\times5\times5\times x\times y}\longrightarrow$ Identify factors that cancel (indicated with line over the top). $\frac{\overline{2}\times2\times\overline{3}\times\overline{3}\times3\times\overline{5}\times \overline{x}\times \overline{y}}{\overline{2}\times\overline{3}\times\overline{3}\times\overline{5}\times5\times5\times \overline{x}\times \overline{y}}\longrightarrow$ Eliminate canceled factors. $\frac{2\times3}{5\times5}$ Simplify. $\frac{6}{25}$