Сократите дробь: (2x^2+9x-18)/(4x^2-9).

Ответ:

\[\frac{2x^{2} + 9x - 18}{4x^{2} - 9} =\]

\[= \frac{2 \cdot (x - 1,5)(x + 6)}{(2x - 3)(2x + 3)} =\]

\[2x^{2} + 9x - 18 = 0\]

\[x_{1} + x_{2} = - 4,5\]

\[x_{1} \cdot x_{2} = - 9\]

\[\Longrightarrow x_{1} = 1,5;\ \ x_{2} = - 6.\]

\[2x^{2} + 9x - 18 =\]

\[= 2 \cdot (x - 1,5)(x + 6) =\]

\[= (2x - 3)(x + 6).\]