What is (|x^2-1|)/(|x^2+x+1|)<1 ?

The solution to (|x^2-1|)/(|x^2+x+1|) 0

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(|x^2-1|)/(|x^2+x+1|)<1

\frac{x ^{2} - 1}{∣ x ^{2} + x + 1 ∣} < 1

- 2 < x < - \frac{1}{2} or x > 0

Solution steps

\frac{x ^{2} - 1}{∣ x ^{2} + x + 1 ∣} < 1

Find positive and negative intervals

x \leq - 1, - 1 < x < 1, x \geq 1

Solve the inequality for each interval

- 2 < x \leq - 1 or (- 1 < x < - \frac{1}{2} or 0 < x < 1) or x \geq 1

Merge Overlapping Intervals

- 2 < x < - \frac{1}{2} or x > 0

x^{2} - 1 \leq 0

∣ 3^{x} - 5 ∣ < 1

x^{2} - 3 ∣ x ∣ - 10 < 0

∣ 3 t - 4 ∣ < 8

∣ 6 x - 12 ∣ < ∣ 2 - x ∣

What is (|x^2-1|)/(|x^2+x+1|)<1 ?
The solution to (|x^2-1|)/(|x^2+x+1|)<1 is -2<x<-1/2 \lor x>0