What is the domain of f(x)=((x-1)(x^2+4))/(x(x+1)) ?

The domain of f(x)=((x-1)(x^2+4))/(x(x+1)) is x 0

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domain of f(x)=((x-1)(x^2+4))/(x(x+1))

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = 0, x = - 1

The function domain

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

What is the domain of f(x)=((x-1)(x^2+4))/(x(x+1)) ?
The domain of f(x)=((x-1)(x^2+4))/(x(x+1)) is x<-1\lor-1<x<0\lor x>0