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

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

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

domain

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

x < - 5 or - 5 < x < 1 or x > 1

Interval Notation

(- \infty, - 5) \cup (- 5, 1) \cup (1, \infty)

Solution steps

Find undefined (singularity) points:

x = - 5, x = 1

The function domain

x < - 5 or - 5 < x < 1 or x > 1

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