Question

If $S$ is the set of all real $x$ such that $\frac{2x}{2x^2+5x+2}>\frac{1}{x+1}$, then $S$ is equal to

• A. $(-\infty ,\frac{-1}{2})$
• B. $(-\infty ,\frac{-2}{3})$
• C. $(-\infty ,\frac{2}{3})$
• D. $(\frac{2}{3},\infty )$

Answer 1

Answer: (B)

$(-\infty ,\frac{-2}{3})$

Given,

$\frac{2x}{2x^2+5x+2}>\frac{1}{x+1}$

or, $2x^2+5x+2<2x^2+2x$

or, $3x+2<0$

or, $x<\frac{-2}{3}$.

So $S=(-\infty ,\frac{-2}{3})$..