Theory of Equations 1 Question 48
49. Find the set of all $x$ for which
$ \frac{2 x}{2 x^{2}+5 x+2}>\frac{1}{x+1} $
(1987, 3M)
Show Answer
Answer:
Correct Answer: 49. ($ x \in(-2,-1) \cup-\frac{2}{3},-\frac{1}{2} $)
Solution:
- Given,
$ \frac{2 x}{2 x^{2}+5 x+2}>\frac{1}{x+1} $
$\Rightarrow \quad \frac{2 x}{(2 x+1)(x+2)}-\frac{1}{(x+1)}>0$
$\Rightarrow \frac{2 x(x+1)-(2 x+1)(x+2)}{(2 x+1)(x+2)(x+1)}>0$ $\Rightarrow \quad \frac{-(3 x+2)}{(2 x+1)(x+1)(x+2)}>0$; using number line rule
$ \therefore \quad x \in(-2,-1) \cup-\frac{2}{3},-\frac{1}{2} $
