for what values of x if ((x(x−1))/(2x+3))>0


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Question Number 33836 by NECx last updated on 25/Apr/18

$f o r w h a t v a l u e s o f x i f$ $\frac{x (x - 1)}{2 x + 3} > 0$
	Answered by Rasheed.Sindhi last updated on 26/Apr/18

	$\frac{x (x - 1)}{2 x + 3} > 0 {\begin{cases} x (x - 1) > 0 \land 2 x + 3 > 0 . . . A \\ x (x - 1) < 0 \land 2 x + 3 < 0 . . . . B \end{cases}$ $A : x > 0 \land x - 1 > 0$ $x > 0 \land x > 1$ $x > 1$ $o r$ $x < 0 \land x - 1 < 0$ $x < 0 \land x < 1$ $x < 0$ $Cont .$
	Commented byNECx last updated on 26/Apr/18

	$p l e a s e I d o n t r e a l l y u n d e r s t a n d$ $t h i s s t y l e . P l e a s e s h e d m o r e$ $l i g h t o n t h e p r i n c i p l e g o v e r n i n g$ $t h i s s t y l e . T h a n k y o u s i r$
	Answered by MJS last updated on 26/Apr/18

	$2 x + 3 \neq 0 \Rightarrow x \neq - \frac{3}{2}$ $1 . 2 x + 3 < 0 \Rightarrow x < - \frac{3}{2}$ $x (x - 1) < 0$ $1.1 . x < 0 \land x - 1 > 0 \Rightarrow no solution$ $1.2 . x > 0 but x < - \frac{3}{2} \Rightarrow no solution$ $2 . 2 x + 3 > 0 \Rightarrow x > - \frac{3}{2}$ $x (x - 1) > 0$ $2.1 . x > 0 \land x - 1 > 0 \Rightarrow x > 1$ $2.2 . x < 0 \land x - 1 < 0 \Rightarrow x < 0$ $- \frac{3}{2} < x < 0 \lor x > 1$ $x \in] - \frac{3}{2}; 0 [\cup] 1; \infty [$
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