Сократите дробь (3a^2-5a-2)/(a^2-4).

Ответ:

\[\frac{3a² - 5a - 2}{a² - 4} = \frac{(a - 2)(3a + 1)}{(a - 2)(a + 2)} = \frac{3a + 1}{a + 2}\]

\[3a^{2} - 5a - 2 = 0\]

\[D = 25 + 24 = 49\]

\[a_{1} = \frac{5 + 7}{6} = \frac{12}{6} = 2;\ \ \ \]

\[a_{2} = \frac{5 - 7}{6} = - \frac{2}{6} = - \frac{1}{3}.\]

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

\[= (a - 2)(3a + 1).\]