Сократите дробь (2^(2n-1)*3^(n+1))/(6*12^n).

\[\frac{2^{2n - 1} \cdot 3^{n + 1}}{6 \cdot 12^{n}} = \frac{\frac{2^{2n}}{2} \cdot 3^{n} \cdot 3}{2 \cdot 3 \cdot 3^{n} \cdot 4^{n}} =\]

\[= \frac{2^{2n}}{2}\ :\left( 2 \cdot 2^{2n} \right) = \frac{2^{2n}}{2} \cdot \frac{1}{2 \cdot 2^{2n}} = \frac{1}{4}.\]