What is the domain of f(x)=(1/x)/(1+1/x) ?

The domain of f(x)=(1/x)/(1+1/x) is x 0

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domain of f(x)=(1/x)/(1+1/x)

domain

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

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 = - 1, x = 0

The function domain

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

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