What is the domain of (2x^3+11x^2+5x)/(2x^2+x) ?

The domain of (2x^3+11x^2+5x)/(2x^2+x) is x 0

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domain of (2x^3+11x^2+5x)/(2x^2+x)

domain

\frac{2 x ^{3} + 11 x ^{2} + 5 x}{2 x ^{2} + x}

x < - \frac{1}{2} or - \frac{1}{2} < x < 0 or x > 0

Interval Notation

(- \infty, - \frac{1}{2}) \cup (- \frac{1}{2}, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - \frac{1}{2}

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < 0 or x > 0

- 2 x^{2} + 40000

f (x) = - 6 x + 18

(x - 1) (x - 6)

\frac{( x ^{2} + 1 )}{x ^{2} - 3 x}

f (x) = \frac{1}{( \frac{1}{x} )}

What is the domain of (2x^3+11x^2+5x)/(2x^2+x) ?
The domain of (2x^3+11x^2+5x)/(2x^2+x) is x<-1/2 \lor-1/2 <x<0\lor x>0