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

The domain of (x/(x-3))/((x/(x-3))-3) is x 9/2

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domain of (x/(x-3))/((x/(x-3))-3)

domain

x < 3 or 3 < x < \frac{9}{2} or x > \frac{9}{2}

Interval Notation

(- \infty, 3) \cup (3, \frac{9}{2}) \cup (\frac{9}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{9}{2}, x = 3

The function domain

x < 3 or 3 < x < \frac{9}{2} or x > \frac{9}{2}

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< 9/2 \lor x> 9/2