What is the domain of x/(ln(x-1)-1) ?

The domain of x/(ln(x-1)-1) is 1 e+1

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domain of x/(ln(x-1)-1)

domain

\frac{x}{ln ( x - 1 ) - 1}

1 < x < e + 1 or x > e + 1

Interval Notation

(1, e + 1) \cup (e + 1, \infty)

Solution steps

Find positive values for logs:

x > 1

Find undefined (singularity) points:

x = e + 1

Combine real regions and undefined points for final function domain

1 < x < e + 1 or x > e + 1

What is the domain of x/(ln(x-1)-1) ?
The domain of x/(ln(x-1)-1) is 1<x<e+1\lor x>e+1