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

The domain of f(x)=(x/(x+2))/(x/(x+2)+2) is x -4/3

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domain of f(x)=(x/(x+2))/(x/(x+2)+2)

domain

x < - 2 or - 2 < x < - \frac{4}{3} or x > - \frac{4}{3}

Interval Notation

(- \infty, - 2) \cup (- 2, - \frac{4}{3}) \cup (- \frac{4}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{4}{3}, x = - 2

The function domain

x < - 2 or - 2 < x < - \frac{4}{3} or x > - \frac{4}{3}

What is the domain of f(x)=(x/(x+2))/(x/(x+2)+2) ?
The domain of f(x)=(x/(x+2))/(x/(x+2)+2) is x<-2\lor-2<x<-4/3 \lor x>-4/3