What is the domain of sqrt((x^2-1)/(x^2+5x+6)) ?

The domain of sqrt((x^2-1)/(x^2+5x+6)) is x = 1

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domain of sqrt((x^2-1)/(x^2+5x+6))

domain

\frac{x ^{2} - 1}{x ^{2} + 5 x + 6}

x < - 3 or - 2 < x \leq - 1 or x \geq 1

Interval Notation

(- \infty, - 3) \cup (- 2, - 1] \cup [1, \infty)

Solution steps

Find non-negative values for radicals:

x < - 3 or - 2 < x \leq - 1 or x \geq 1

Find undefined (singularity) points:

x = - 2, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 2 < x \leq - 1 or x \geq 1

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

sin (7 x)

(11.13) (8.17)

y = 2 cos (2 π (x + \frac{2 π}{3})) - 5

5 x + 2 y = 4

What is the domain of sqrt((x^2-1)/(x^2+5x+6)) ?
The domain of sqrt((x^2-1)/(x^2+5x+6)) is x<-3\lor-2<x<=-1\lor x>= 1