Сократите дробь (3a^2-11a-4)/(a^2-16).

Ответ:

\[\frac{3a^{2} - 11a - 4}{a^{2} - 16} = \frac{(3a + 1)(a - 4)}{(a - 4)(a + 4)} = \frac{3a + 1}{a + 4}\]

\[3a^{2} - 11a - 4 = 3 \cdot \left( a + \frac{1}{3} \right)(a - 4) =\]

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

\[D = 121 + 48 = 169\]

\[a_{1} = \frac{11 + 13}{6} = 4;\]

\[a_{2} = \frac{11 - 13}{6} = - \frac{2}{6} = - \frac{1}{3}.\]