Сократите дробь (4a^2+a-3)/(a^2-1).

Ответ:

\[\frac{4a² + a - 3}{a² - 1} = \frac{(4a - 3)(a + 1)}{(a - 1)(a + 1)} = \frac{4a - 3}{a - 1}\]

\[4a² + a - 3 = 0\]

\[D = 1 + 48 = 49\]

\[a_{1} = \frac{- 1 + 7}{8} = \frac{6}{8} = \frac{3}{4};\ \ \ \]

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

\[4a^{2} + a - 3 = 4 \cdot \left( a - \frac{3}{4} \right)(a + 1) =\]

\[= (4a - 3)(a + 1).\]