Answer
$\frac{5}{2z}$
Work Step by Step
$\frac{10x\times12\times25y}{2z\times30x\times20y}\longrightarrow$ Use prime factorization.
$\frac{2\times5\times x\times2\times2\times3\times5\times5\times y}{2\times z\times2\times3\times5\times x\times2\times2\times5\times y}\longrightarrow$ Reorder factors.
$\frac{2\times2\times2\times3\times5\times5\times5\times x\times y}{2\times2\times2\times2\times3\times5\times 5\times x\times y\times z}\longrightarrow$ Identify factors that cancel (indicated with a line over).
$\frac{\overline{2\times2\times2\times3\times5\times5}\times5\times \overline{x}\times \overline{y}}{\overline{2\times2\times2}\times2\times\overline{3\times5\times 5}\times \overline{x}\times \overline{y}\times z}\longrightarrow$ Eliminate canceled factors.
$\frac{5}{2z}$
