Сократите дробь: (25a^2+10a+1)/(5a^2-9a-2).

Ответ:

\[5a^{2} - 9a - 2 = 0\]

\[D = 81 + 40 = 121\]

\[a_{1} = \frac{9 + 11}{10} = 2;\ \ \ \ \]

\[a_{2} = \frac{9 - 11}{10} = - \frac{2}{10} = - \frac{1}{5}.\]

\[5a^{2} - 9a - 2 =\]

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

\[= (a - 2)(5a + 1).\]