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Inequalities Involving Modulus Function

Solve the fol...

Question

Solve the following inequality:
$\frac{x^{2} - 9}{3 x - x^{2} - 24} < 0$

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Solution

$\frac{x^{2} - 9}{3 x - x^{2} - 24} < 0$
$\frac{x^{2} - 9}{x^{2} - 3 x + 24} > 0$
As discriminant of $x^{2} - 3 x + 24 < 0$ is $x^{2} - 3 x + 24 > 0 \forall x ϵ R$
$x^{2} - 3 x + 24 > 0 \forall x ϵ R$
$x^{2} - 9 > 0$
$(x - 3) (x + 3) > 0$
$x ϵ (- 3, 3)$

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Inequalities Involving Modulus Function

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