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2x/ 2x²+5x+2 > 1/x+1

$\frac{2 x}{2 x^{2} + 5 x + 2} > \frac{1}{x + 1} \Rightarrow 2 x (x + 1) > 2 x^{2} + 5 x + 2 \Rightarrow 2 x^{2} + 2 x > 2 x^{2} + 5 x + 2 \Rightarrow 2 x > 5 x + 2 \Rightarrow 5 x - 2 x + 2 < 0 \Rightarrow 3 x + 2 < 0 \Rightarrow 3 x < - 2 \Rightarrow x < - \frac{2}{3} T h u s, x \in (- \infty, - \frac{2}{3})$

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