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

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

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

domain

x < - 5 or - 5 < x \leq - 1 or 1 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 1

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - 5 < x \leq - 1 or 1 \leq x < 5 or x > 5

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