What is the domain of h(x)=(x-3)/(x^3-9x) ?

The domain of h(x)=(x-3)/(x^3-9x) is x 3

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domain of h(x)=(x-3)/(x^3-9x)

domain

h (x) = \frac{x - 3}{x ^{3} - 9 x}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 0, x = - 3, x = 3

The function domain

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

f (x) = \frac{( x + 5 )}{( x ^{2} + 5 x + 6 )}

f (x) = \frac{x - 2}{x + 4}

2 5^{x - 4} + 4

y = (x + 1)^{2} - 2

2 x^{2} - 8 x + 8

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