What is ((x^2-|x|-2))/((2|x|-x^2-2))>2 ?

The solution to ((x^2-|x|-2))/((2|x|-x^2-2))>2 is -1<x<-2/3 \lor 2/3 <x<1

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((x^2-|x|-2))/((2|x|-x^2-2))>2

\frac{( x ^{2} - ∣ x ∣ - 2 )}{( 2 ∣ x ∣ - x ^{2} - 2 )} > 2

- 1 < x < - \frac{2}{3} or \frac{2}{3} < x < 1

Solution steps

\frac{x ^{2} - ∣ x ∣ - 2}{2 ∣ x ∣ - x ^{2} - 2} > 2

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

- 1 < x < - \frac{2}{3} or \frac{2}{3} < x < 1

∣ 3 d - 3 ∣ > 12

∣ x - 4 ∣ + 2 ∣ x - 3 ∣ \geq 4

∣ 2 x + 7 ∣ < ∣ 5 ∣

(1 + x^{2}) \geq 1 - x^{2}

∣ x + 1 ∣ + ∣ x - 4 ∣ > 7

What is ((x^2-|x|-2))/((2|x|-x^2-2))>2 ?
The solution to ((x^2-|x|-2))/((2|x|-x^2-2))>2 is -1<x<-2/3 \lor 2/3 <x<1