What is the domain of (9x^2-1)/(9x^3+6x^2+x) ?

The domain of (9x^2-1)/(9x^3+6x^2+x) is x 0

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domain of (9x^2-1)/(9x^3+6x^2+x)

domain

\frac{9 x ^{2} - 1}{9 x ^{3} + 6 x ^{2} + x}

x < - \frac{1}{3} or - \frac{1}{3} < x < 0 or x > 0

Interval Notation

(- \infty, - \frac{1}{3}) \cup (- \frac{1}{3}, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - \frac{1}{3}

The function domain

x < - \frac{1}{3} or - \frac{1}{3} < x < 0 or x > 0

What is the domain of (9x^2-1)/(9x^3+6x^2+x) ?
The domain of (9x^2-1)/(9x^3+6x^2+x) is x<-1/3 \lor-1/3 <x<0\lor x>0