What is the domain of 1/(3-(\frac{x){x-1})} ?

The domain of 1/(3-(\frac{x){x-1})} is x 3/2

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domain of 1/(3-(\frac{x){x-1})}

domain

x < 1 or 1 < x < \frac{3}{2} or x > \frac{3}{2}

Interval Notation

(- \infty, 1) \cup (1, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{3}{2}, x = 1

The function domain

x < 1 or 1 < x < \frac{3}{2} or x > \frac{3}{2}

What is the domain of 1/(3-(\frac{x){x-1})} ?
The domain of 1/(3-(\frac{x){x-1})} is x<1\lor 1<x< 3/2 \lor x> 3/2