What is the domain of f(x)=(12x^4-12x)/((x^3+2)^3) ?

The domain of f(x)=(12x^4-12x)/((x^3+2)^3) is x -\sqrt[3]{2}

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domain of f(x)=(12x^4-12x)/((x^3+2)^3)

domain

f (x) = \frac{12 x ^{4} - 12 x}{( x ^{3} + 2 ) ^{3}}

x < - 32 or x > - 32

Interval Notation

(- \infty, - 32) \cup (- 32, \infty)

Solution steps

Find undefined (singularity) points:

x = - 32

The function domain

x < - 32 or x > - 32

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

f (x) = \frac{( 2 x - 1 )}{2 x ^{2} - 5 x - 6}

f (x) = x^{2} + 4 x - 6

\frac{( x + 8 )}{( x + 4 )}

f (x) = 4 - 3 x + 2 x

What is the domain of f(x)=(12x^4-12x)/((x^3+2)^3) ?
The domain of f(x)=(12x^4-12x)/((x^3+2)^3) is x<-\sqrt[3]{2}\lor x>-\sqrt[3]{2}