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

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

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

\frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )} > 1

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

Interval Notation

(- \infty, - 2) \cup (- \frac{1}{2}, 0)

Decimal Notation

x < - 2 or - 0.5 < x < 0

Solution steps

\frac{x ^{2} - 1}{x ^{2} + x + 1} > 1

Apply absolute rule: If

∣ u ∣ > a, a > 0

then

u < - a

u > a

\frac{x ^{2} - 1}{x ^{2} + x + 1} < - 1 or \frac{x ^{2} - 1}{x ^{2} + x + 1} > 1

\frac{x ^{2} - 1}{x ^{2} + x + 1} < - 1 or \frac{x ^{2} - 1}{x ^{2} + x + 1} > 1

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

∣ x + 3 ∣ < 0.01

∣ x - 1 ∣ > 2 ∣ x - 4 ∣

\frac{( 3 x - 5 )}{2} \geq 7

∣ 1 - x ∣ - ∣ 4 + x ∣ < 0

∣ x + 1 ∣ > 1

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