Сократите дробь (a+b-5b^2+5a^2)/(5a+5b-1).

Ответ:

\[\frac{a + b - 5b^{2} + 5a^{2}}{5a + 5b - 1} = \frac{(a + b) - 5 \cdot \left( b^{2} - a^{2} \right)}{5a + 5b - 1} =\]

\[= \frac{(a + b)\left( 1 - 5 \cdot (b - a) \right)}{5a + 5b - 1} =\]

\[= \frac{(a + b)(1 - 5b + 5a)}{5a + 5b - 1} =\]

\[= \frac{(a + b)(5a - 5b + 1)}{5a + 5b - 1} =\]

\[= \frac{- (a + b)( - 5a + 5b - 1)}{5a + 5b - 1}\]