Сократите дробь (2a^2+9a-5)/(a^2-25).

Ответ:

\[\frac{2a^{2} + 9a - 5}{a^{2} - 25} = \frac{(2a - 1)(a + 5)}{(a - 5)(a + 5)} = \frac{2a - 1}{a - 5}\]

\[2a^{2} + 9a - 5 = 2 \cdot \left( a - \frac{1}{2} \right)(a + 5) =\]

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

\[D = 81 + 40 = 121\]

\[a_{1} = \frac{- 9 + 11}{4} = \frac{2}{4} = \frac{1}{2};\]

\[a_{2} = \frac{- 9 - 11}{4} = - \frac{20}{4} = - 5.\]