What is (x^2-4|x|+3)/(x(x+4))=>0 ?

The solution to (x^2-4|x|+3)/(x(x+4))=>0 is x 3

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(x^2-4|x|+3)/(x(x+4))=>0

\frac{x ^{2} - 4 ∣ x ∣ + 3}{x ( x + 4 )} => 0

x < - 4 or - 3 < x < - 1 or 0 < x < 1 or x > 3

Interval Notation

(- \infty, - 4) \cup (- 3, - 1) \cup (0, 1) \cup (3, \infty)

Solution steps

\frac{x ^{2} - 4 ∣ x ∣ + 3}{x ( x + 4 )} > 0

Find positive and negative intervals

x < 0, x \geq 0

Solve the inequality for each interval

x < - 4 or - 3 < x < - 1 or (0 < x < 1 or x > 3)

Merge Overlapping Intervals

x < - 4 or - 3 < x < - 1 or 0 < x < 1 or x > 3

∣ x - 3 ∣ + 2 ∣ x + 1 ∣ > 4

\frac{x + 1}{x} < \frac{5}{2}

2 - 4 ∣ 2 x + 4 ∣ < - 26

∣ 2 x - a ∣ < 3

x^{2} + 2 ∣ x + 3 ∣ - 10 \leq 0

What is (x^2-4|x|+3)/(x(x+4))=>0 ?
The solution to (x^2-4|x|+3)/(x(x+4))=>0 is x<-4\lor-3<x<-1\lor 0<x<1\lor x>3