Сократить дробь: (2x^2+5x-3)/(x^2-9).

Ответ:

\[\frac{2x^{2} + 5x - 3}{x^{2} - 9} =\]

\[= \frac{(2x - 1)(x + 3)}{(x - 3)(x + 3)} = \frac{2x - 1}{x - 3}\]

\[2x^{2} + 5x - 3 =\]

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

\[= (2x - 1)(x + 3)\]

\[D = 25 + 24 = 49\]

\[x_{1} = \frac{- 5 + 7}{4} = \frac{1}{2};\]

\[x_{2} = \frac{- 5 - 7}{4} = - 3.\]