What is (|x-3|)/(x^4-9x^2)<0 ?

The solution to (|x-3|)/(x^4-9x^2)<0 is -3<x<0\lor 0<x<3

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(|x-3|)/(x^4-9x^2)<0

\frac{∣ x - 3 ∣}{x ^{4} - 9 x ^{2}} < 0

- 3 < x < 0 or 0 < x < 3

Interval Notation

(- 3, 0) \cup (0, 3)

Solution steps

\frac{∣ x - 3 ∣}{x ^{4} - 9 x ^{2}} < 0

∣ x - 3 ∣ \geq 0

\frac{a}{b} < 0 and a \geq 0

then

a > 0 and b < 0

∣ x - 3 ∣ > 0 and (x^{4} - 9 x^{2}) < 0

∣ x - 3 ∣ > 0 : x < 3 or x > 3

x^{4} - 9 x^{2} < 0 : - 3 < x < 0 or 0 < x < 3

Combine the intervals

(x < 3 or x > 3) and (- 3 < x < 0 or 0 < x < 3)

Merge Overlapping Intervals

- 3 < x < 0 or 0 < x < 3

6 k^{2} + k - 1

6 q^{2} - 3 q = 5 q^{2} - 5 q + 24

(\frac{1}{2})^{1.5}

f = 30 (1.149)^{5}

n^{2} - 6 n + 9

What is (|x-3|)/(x^4-9x^2)<0 ?
The solution to (|x-3|)/(x^4-9x^2)<0 is -3<x<0\lor 0<x<3