What is the domain of ((2x^2+x))/(x^3+8x^2+15x) ?

The domain of ((2x^2+x))/(x^3+8x^2+15x) is x 0

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domain of ((2x^2+x))/(x^3+8x^2+15x)

domain

\frac{( 2 x ^{2} + x )}{x ^{3} + 8 x ^{2} + 15 x}

x < - 5 or - 5 < x < - 3 or - 3 < x < 0 or x > 0

Interval Notation

(- \infty, - 5) \cup (- 5, - 3) \cup (- 3, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 3, x = - 5

The function domain

x < - 5 or - 5 < x < - 3 or - 3 < x < 0 or x > 0

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

y = 1 - cos (x)

(21, - 30), (3, 8)

y = 1 - x^{2}

(6, - 5), (12, 15)

What is the domain of ((2x^2+x))/(x^3+8x^2+15x) ?
The domain of ((2x^2+x))/(x^3+8x^2+15x) is x<-5\lor-5<x<-3\lor-3<x<0\lor x>0