solve ((2x)/(x^2 +1))<((3x+1)/(2(x^2 +1)))


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Question Number 27976 by NECx last updated on 18/Jan/18

$s o l v e$ $\frac{2 x}{x^{2} + 1} < \frac{3 x + 1}{2 (x^{2} + 1)}$
Commented byabdo imad last updated on 18/Jan/18

$d u e t o x^{2} + 1 > 0 (e) \Leftrightarrow 2 x < \frac{3 x + 1}{2}$ $\Leftrightarrow 4 x - 3 x - 1 < 0 \Leftrightarrow x - 1 < 0 \Leftrightarrow x < 1 \Leftrightarrow x \in] - \propto, 1 [$
	Answered by Rasheed.Sindhi last updated on 18/Jan/18

	$x^{2} + 1 > 0$ $Multiplying by 2 (x^{2} + 1) to both$ $sides$ $\frac{2 x}{x^{2} + 1} < \frac{3 x + 1}{2 (x^{2} + 1)} \Rightarrow 4 x < 3 x + 1$ $x < 1$
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