What is the domain of (x^3+3x^2+2x)/(3x^3+3x^2-6x) ?

The domain of (x^3+3x^2+2x)/(3x^3+3x^2-6x) is x 1

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domain of (x^3+3x^2+2x)/(3x^3+3x^2-6x)

domain

\frac{x ^{3} + 3 x ^{2} + 2 x}{3 x ^{3} + 3 x ^{2} - 6 x}

x < - 2 or - 2 < x < 0 or 0 < x < 1 or x > 1

Interval Notation

(- \infty, - 2) \cup (- 2, 0) \cup (0, 1) \cup (1, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = 1, x = - 2

The function domain

x < - 2 or - 2 < x < 0 or 0 < x < 1 or x > 1

f (x) = - \frac{1}{2} x^{2} - 4 x + 10

f (x) = (x - 13)^{2}, x \leq 13

y = 3 sin (2 x)

y = x

f (x) = 3 x^{2} - 5 x + 2

What is the domain of (x^3+3x^2+2x)/(3x^3+3x^2-6x) ?
The domain of (x^3+3x^2+2x)/(3x^3+3x^2-6x) is x<-2\lor-2<x<0\lor 0<x<1\lor x>1