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

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

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

domain

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

x < - 3 or - 3 < x < - 1 or - 1 < x < 1 or x > 1

Interval Notation

(- \infty, - 3) \cup (- 3, - 1) \cup (- 1, 1) \cup (1, \infty)

Solution steps

Find undefined (singularity) points:

x = - 3, x = - 1, x = 1

The function domain

x < - 3 or - 3 < x < - 1 or - 1 < x < 1 or x > 1

y = 2 x^{2} + x - 3

\frac{1}{4} cos (\frac{1}{4} x - \frac{π}{12})

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

f (x) = 36 - x^{2}

\frac{x + x ( 2 x ^{2} - 5 )}{2 x ^{2} - 5}

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