Q. If $\frac{2x}{2x^{2} + 5x + 2} > \frac{1}{x + 1}$, then
A) $- 2 > x > - 1$
B) $- 2 \geq x \geq - 1$
C) $- 2 < x < - 1$
D) $- 2 < x \leq - 1$
Explanation
(c)
Given, $\frac{2x}{(2x + 1)(x + 2)} - \frac{1}{(x + 1)} > 0$
$\Rightarrow \ \ \frac{- 3x - 2}{(x + 1)(x + 2)(2x + 1)} > 0$
Equating each factor equal to 0, we have
$x = - 2,\ - 1,\ - \frac{2}{3},\ - \frac{1}{2}$
It is clear $- \frac{2}{3} < x < - \frac{1}{2}$ or $- 2 < x < - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.