The number of integral values of $x,$ satisfying the inequality $\frac{(| x | + 3) (4 - | x |)}{x^{2} - | x |} > 0$ is

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Solution

$\frac{(| x | + 3) (4 - | x |)}{x^{2} - | x |} > 0$
$\Rightarrow \frac{(| x | + 3) (| x | - 4)}{| x | (| x | - 1)} < 0$
$\Rightarrow \frac{| x | - 4}{| x | - 1} < 0 (∵ | x | + 3 > 0, | x | > 0 \forall x \in R - {0})$
$\Rightarrow | x | \in (1, 4)$
$\Rightarrow x \in (- 4, - 1) \cup (1, 4)$
Integral values of $x$ are ${- 3, - 2, 2, 3}$

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