What is the domain of (sqrt(x+4))/((x+2)(x-5)) ?

The domain of (sqrt(x+4))/((x+2)(x-5)) is -4 5

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domain of (sqrt(x+4))/((x+2)(x-5))

domain

\frac{x + 4}{( x + 2 ) ( x - 5 )}

- 4 \leq x < - 2 or - 2 < x < 5 or x > 5

Interval Notation

[- 4, - 2) \cup (- 2, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = - 2, x = 5

Combine real regions and undefined points for final function domain

- 4 \leq x < - 2 or - 2 < x < 5 or x > 5

f (x) = \frac{( 24 x ^{2} + 6 x )}{( 2 x + 1 )}

f (x) = \frac{3}{4 + x}

4 x + 1

y = - 15

What is the domain of (sqrt(x+4))/((x+2)(x-5)) ?
The domain of (sqrt(x+4))/((x+2)(x-5)) is -4<= x<-2\lor-2<x<5\lor x>5