What is the domain of ((x-5)(x+1))/((x+1)(x-2)x) ?

The domain of ((x-5)(x+1))/((x+1)(x-2)x) is x 2

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domain of ((x-5)(x+1))/((x+1)(x-2)x)

domain

\frac{( x - 5 ) ( x + 1 )}{( x + 1 ) ( x - 2 ) x}

x < - 1 or - 1 < x < 0 or 0 < x < 2 or x > 2

Interval Notation

(- \infty, - 1) \cup (- 1, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = - 1, x = 2, x = 0

The function domain

x < - 1 or - 1 < x < 0 or 0 < x < 2 or x > 2

What is the domain of ((x-5)(x+1))/((x+1)(x-2)x) ?
The domain of ((x-5)(x+1))/((x+1)(x-2)x) is x<-1\lor-1<x<0\lor 0<x<2\lor x>2