What is the domain of f(x)=(x/(x+9))/(x/(x+9)+9) ?

The domain of f(x)=(x/(x+9))/(x/(x+9)+9) is x -81/10

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domain of f(x)=(x/(x+9))/(x/(x+9)+9)

domain

f (x) = \frac{\frac{x}{x + 9}}{\frac{x}{x + 9} + 9}

x < - 9 or - 9 < x < - \frac{81}{10} or x > - \frac{81}{10}

Interval Notation

(- \infty, - 9) \cup (- 9, - \frac{81}{10}) \cup (- \frac{81}{10}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{81}{10}, x = - 9

The function domain

x < - 9 or - 9 < x < - \frac{81}{10} or x > - \frac{81}{10}

What is the domain of f(x)=(x/(x+9))/(x/(x+9)+9) ?
The domain of f(x)=(x/(x+9))/(x/(x+9)+9) is x<-9\lor-9<x<-81/10 \lor x>-81/10