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Find the range of values of \(x\) that satisfy the inequality \(\dfrac{x^2-4}{(x-5)(x^2-9)}<0.\)

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Find the range of values of \(x\) that satisfy the inequality \(\dfrac{x^2-4}{(x-5)(x^2-9)}<0.\)

by Vincen » Thu Nov 26, 2020 11:52 am

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Find the range of values of \(x\) that satisfy the inequality \(\dfrac{x^2-4}{(x-5)(x^2-9)}<0.\)

A. \(x < -3\) or \(3 < x < 5\)

B. \(x < -3\) or \(-2 < x < 2\)

C. \(-2 < x < 2\) or \(3 < x < 5\)

D. \(x < -3\) or \(-2 < x < 2\) or \(3 < x < 5\)

E. \(x < -3\)

Answer: D

Source: e-GMAT
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Re: Find the range of values of \(x\) that satisfy the inequality \(\dfrac{x^2-4}{(x-5)(x^2-9)}<0.\)

by deloitte247 » Sat Nov 28, 2020 12:02 pm
$$Find\ the\ range\ of\ values\ that\ satisfy\ \frac{x^2-4}{\left(x5\right)\left(x^2-9\right)}<0$$
$$\frac{\left(x-2\right)\left(x+2\right)}{\left(x-5\right)\left(x-3\right)\left(x+3\right)}<0$$
$$With\ this,\ the\ zero\ points\ of\ x\ are;$$
$$x-2<0\ =\ x<2$$
$$x+2<0\ =\ x<-2$$
$$x-5<0\ =\ x<5$$
$$x-3<0\ =\ x<3$$
$$3+3<0\ =\ x<-3$$
$$so\ value\ of\ x\ is\ between\ -3\ and\ 5$$
$$for\ -3,\ -2,\ 2,\ 3\ and\ 5,\ the\ option\ that\ fit\ the\ range\ of\ x\ is;$$
$$x<-3\ or\ -2\ <x<2\ or\ 3\ <x<5$$
$$Answer\ =\ D$$
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