What is the domain of ((x/(x+5)))/((x/(x+5))+5) ?

The domain of ((x/(x+5)))/((x/(x+5))+5) is x -25/6

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domain of ((x/(x+5)))/((x/(x+5))+5)

domain

x < - 5 or - 5 < x < - \frac{25}{6} or x > - \frac{25}{6}

Interval Notation

(- \infty, - 5) \cup (- 5, - \frac{25}{6}) \cup (- \frac{25}{6}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{25}{6}, x = - 5

The function domain

x < - 5 or - 5 < x < - \frac{25}{6} or x > - \frac{25}{6}

What is the domain of ((x/(x+5)))/((x/(x+5))+5) ?
The domain of ((x/(x+5)))/((x/(x+5))+5) is x<-5\lor-5<x<-25/6 \lor x>-25/6