Сократите дробь (1-3x+3y)/(3x^2-3y^2-x-y).

Ответ:

\[\frac{1 - 3x + 3y}{3x^{2} - 3y^{2} - x - y} =\]

\[= \frac{1 - 3x + 3y}{3 \cdot \left( x^{2} - y^{2} \right) - (x + y)} =\]

\[= \frac{1 - 3x + 3y}{(x + y)\left( 3 \cdot (x - y) - 1 \right)} =\]

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

\[= \frac{1 - 3x + 3y}{- (x + y)(1 - 3x + 3y)} = - \frac{1}{x + y}.\]