Сократите дробь: (x^3+8)/(4x^2+7x-2).

\[4x^{2} + 7x - 2 = 0\]

\[x_{1} + x_{2} = - \frac{7}{4},\ \ x_{1} \cdot x_{2} = - \frac{1}{2}\]

\[\Longrightarrow x_{1} = \frac{1}{4},\ \ x_{2} = - 2\]

\[4x^{2} + 7x - 2 =\]

\[= 4 \cdot \left( x - \frac{1}{4} \right)(x + 2) =\]

\[= (4x - 1)(x + 2).\]