Сократите дробь: (4a^2+a-3)/(a^2-1).

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

\[= \frac{4a - 3}{a - 1}.\]

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

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

\[D = 1 + 48 = 49\]

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

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