Explanation

(c)
Given that, $\frac{2x}{2x^{2} + 5x + 2} > \frac{1}{(x + 1)}$
$\Rightarrow \frac{2x}{(2x + 1)(x + 2)} > \frac{1}{(x + 1)}$
$\Rightarrow \ \frac{2x}{(2x + 1)(x + 2)} - \frac{1}{(x + 1)} > 0$
$\Rightarrow \ \frac{2x(x + 1) - (2x + 1)(x + 2)}{(x + 1)(2x + 1)(x + 2)} > 0$
$\Rightarrow \ \frac{2x^{2} + 2x - 2x^{2} - 4x - x - 2}{(x + 1)(2x + 1)(x + 2)} > 0$
$\Rightarrow \ \frac{- 3x - 2}{(x + 1)(2x + 1)(x + 2)} > 0$
Equating each factor equal to 0, we have
$x = - 2,\ - 1,\ - \frac{2}{3},\ - \frac{1}{2}$
It is clear that$- \frac{2}{3} < x < - \frac{1}{2}\ or\ - 2 < x - 1$.