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

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

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

domain

y = \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

\frac{4 x}{x + 1}

3 x - 9, - 1 \leq x \leq 7

3 1 - x

f (x) = - \frac{1}{8 x - 3 - 4 x ^{2}}

arccos (ln (3 x))

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