What is the domain of (x-4)/(x^3-81x) ?

The domain of (x-4)/(x^3-81x) is x 9

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domain of (x-4)/(x^3-81x)

domain

\frac{x - 4}{x ^{3} - 81 x}

x < - 9 or - 9 < x < 0 or 0 < x < 9 or x > 9

Interval Notation

(- \infty, - 9) \cup (- 9, 0) \cup (0, 9) \cup (9, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 9, x = 9

The function domain

x < - 9 or - 9 < x < 0 or 0 < x < 9 or x > 9

What is the domain of (x-4)/(x^3-81x) ?
The domain of (x-4)/(x^3-81x) is x<-9\lor-9<x<0\lor 0<x<9\lor x>9