What is the domain of (5x)/((x-10)sqrt(x^2-x-30)) ?

The domain of (5x)/((x-10)sqrt(x^2-x-30)) is x 10

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domain of (5x)/((x-10)sqrt(x^2-x-30))

domain

\frac{5 x}{( x - 10 ) x ^{2} - x - 30}

x < - 5 or 6 < x < 10 or x > 10

Interval Notation

(- \infty, - 5) \cup (6, 10) \cup (10, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 6

Find undefined (singularity) points:

x = 10, x = 6, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or 6 < x < 10 or x > 10

f (x) = \frac{x + 9}{x ^{2} - x - 42}

f (x) = \frac{x ^{2} + 2 x - 3}{x ^{3} - 4 x}

f (x) = \frac{t}{9 - t ^{2}}

f (x) = x - x + 8

x^{3} + 2 x

What is the domain of (5x)/((x-10)sqrt(x^2-x-30)) ?
The domain of (5x)/((x-10)sqrt(x^2-x-30)) is x<-5\lor 6<x<10\lor x>10