What is the domain of (x/(x+3))/(x/(x+3)+3) ?

The domain of (x/(x+3))/(x/(x+3)+3) is x -9/4

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domain of (x/(x+3))/(x/(x+3)+3)

domain

\frac{\frac{x}{x + 3}}{\frac{x}{x + 3} + 3}

x < - 3 or - 3 < x < - \frac{9}{4} or x > - \frac{9}{4}

Interval Notation

(- \infty, - 3) \cup (- 3, - \frac{9}{4}) \cup (- \frac{9}{4}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{9}{4}, x = - 3

The function domain

x < - 3 or - 3 < x < - \frac{9}{4} or x > - \frac{9}{4}

What is the domain of (x/(x+3))/(x/(x+3)+3) ?
The domain of (x/(x+3))/(x/(x+3)+3) is x<-3\lor-3<x<-9/4 \lor x>-9/4