What is the domain of (sqrt(x+6)-x)/(x^3-3x^2) ?

The domain of (sqrt(x+6)-x)/(x^3-3x^2) is -6 3

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domain of (sqrt(x+6)-x)/(x^3-3x^2)

domain

\frac{x + 6 - x}{x ^{3} - 3 x ^{2}}

- 6 \leq x < 0 or 0 < x < 3 or x > 3

Interval Notation

[- 6, 0) \cup (0, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 6

Find undefined (singularity) points:

x = 0, x = 3

Combine real regions and undefined points for final function domain

- 6 \leq x < 0 or 0 < x < 3 or x > 3

\frac{3 x ^{2} - 6}{x ^{2} - 1}

x^{3} + x^{2} - 2 x

3 x + 14

ln (- x)

f (x) = \frac{x + 3}{4} - 5

What is the domain of (sqrt(x+6)-x)/(x^3-3x^2) ?
The domain of (sqrt(x+6)-x)/(x^3-3x^2) is -6<= x<0\lor 0<x<3\lor x>3