Найдите значение дроби (x-3y)/(6x^2-54y^2), если x+3y=1/4.

\[\frac{x - 3y}{6x^{2} - 54y^{2}} = \frac{x - 3y}{6\left( x^{2} - 9y^{2} \right)} =\]

\[= \frac{x - 3y}{6(x - 3y)(x + 3y)} =\]

\[= \frac{1}{6(x + 3y)};\]

\[x + 3y = \frac{1}{4}:\]

\[\frac{1}{6 \cdot \frac{1}{4}} = 1\ :\frac{6}{4} = 1 \cdot \frac{4}{6} = \frac{2}{3}.\]