Сократите дробь (3a^2+7a-6)/(a^2-9).

Ответ:

\[\frac{3a^{2} + 7a - 6}{a^{2} - 9} = \frac{(3a - 2)(a + 3)}{(a - 3)(a + 3)} = \frac{3a - 2}{a - 3}\]

\[3a^{2} + 7a - 6 = 3 \cdot \left( a - \frac{2}{3} \right)(a + 3) =\]

\[= (3a - 2)(a + 3)\]

\[D = 49 + 72 = 121\]

\[a_{1} = \frac{- 7 + 11}{6} = \frac{4}{6} = \frac{2}{3};\]

\[a_{2} = \frac{- 7 - 11}{6} = - \frac{18}{6} = - 3.\]