What is the domain of f(x)= x/((x-1)^2-1) ?

The domain of f(x)= x/((x-1)^2-1) is x 2

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domain of f(x)= x/((x-1)^2-1)

domain

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

x < 0 or 0 < x < 2 or x > 2

Interval Notation

(- \infty, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = 0

The function domain

x < 0 or 0 < x < 2 or x > 2

f (x) = (3 - 2 x)

f (x) = \frac{3}{x ^{2} + 2 x - 35}

f (x) = \frac{x - 3}{x + 4}

1 + \frac{1}{x} - \frac{1}{x ^{2}}

f (x) = 4 - 2 x^{2}

What is the domain of f(x)= x/((x-1)^2-1) ?
The domain of f(x)= x/((x-1)^2-1) is x<0\lor 0<x<2\lor x>2