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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 2

Find undefined (singularity) points:

x = 2, x = - 3

Combine real regions and undefined points for final function domain

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

f (x) = \frac{2 ( x + 2 )}{3 x + 17}

f (x) = - 4 (x - 7) (x - 3)

g (x) = 16 - x^{4}

\frac{2 x + 10}{x ^{2} - 4 x - 5}

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

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