Сократите дробь: (4a^2+12a+9)/(2a^2+a-3).

Ответ:

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

\[D = 1 + 24 = 25\]

\[a_{1} = \frac{- 1 + 5}{4} = \frac{4}{4} = 1;\ \ \ \]

\[a_{2} = \frac{- 1 - 5}{4} = - \frac{6}{4} = - \frac{3}{2}.\]

\[2a^{2} + a - 3 =\]

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

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