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ind the range of values of x that satisfy the inequality (x2

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ind the range of values of x that satisfy the inequality (x2

by BTGmoderatorDC » Mon May 06, 2019 3:53 pm

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Find the range of values of x that satisfy the inequality ((x2−4)/(x−5)(x2−9))<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

OA D

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by deloitte247 » Sun May 12, 2019 9:58 am
$$\frac{\left(x^2-4\right)}{\left(x-5\right)\left(x-9\right)}<0$$
$$where\ \left(x^2-4\right)=\left(x+2\right)\left(x-2\right)\ and\ \left(x^2-9\right)=\left(x+3\right)\left(x-3\right)$$
$$Therefore,\ \frac{\left(x+2\right)\left(x-2\right)}{\left(x-5\right)\left(x+3\right)\left(x-3\right)}\ <0$$
$$Required\ range\ =>\ x<-3\ or\ -2<x<2\ or\ 3<x<5$$

Answer = option D
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