Сократите дробь: (3+14b-5b^2)/(3b-b^2).

Ответ:

\[\frac{3 + 14b - 5b^{2}}{3b - b^{2}} =\]

\[= \frac{- \left( 5b^{2} - 14b - 3 \right)}{- b(b - 3)} =\]

\[= \frac{5 \cdot \left( b + \frac{1}{5} \right)(b - 3)}{b(b - 3)} = \frac{5b + 1}{b}\]

\[5b^{2} - 14b - 3 = 0\]

\[D = 49 + 15 = 64\]

\[b_{1} = \frac{7 + 8}{5} = 3;\ \ \ \]

\[b_{2} = \frac{7 - 8}{5} = - \frac{1}{5}.\]