Сократите дробь (5a^2+3a-2)/(a^2-1).

Ответ:

\[\frac{5a^{2} + 3a - 2}{a^{2} - 1} = \frac{(5a - 2)(a + 1)}{(a - 1)(a + 1)} = \frac{5a - 2}{a - 1}\]

\[5a^{2} + 3a - 2 = 5 \cdot \left( a - \frac{2}{5} \right)(a + 1) =\]

\[= (5a - 2)(a + 1)\]

\[D = 9 + 40 = 49\]

\[a_{1} = \frac{- 3 + 7}{10} = \frac{4}{10} = \frac{2}{5};\]

\[a_{2} = \frac{- 3 - 7}{10} = - 1.\]