What is the domain of sqrt(x+5)-(sqrt(3-x))/x ?

The domain of sqrt(x+5)-(sqrt(3-x))/x is -5<= x<0\lor 0<x<= 3

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domain of sqrt(x+5)-(sqrt(3-x))/x

domain

x + 5 - \frac{3 - x}{x}

- 5 \leq x < 0 or 0 < x \leq 3

Interval Notation

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 3

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 5 \leq x < 0 or 0 < x \leq 3

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

\frac{2 x ^{3} - x ^{2} - 18 x + 9}{x ^{2} + 4 x + 3}

f (x) = - 4 x^{2} + 16 x - 10

f (x) = \frac{\frac{1}{x}}{\frac{1}{x}}

5 x + 6 + 1 - 8 x

What is the domain of sqrt(x+5)-(sqrt(3-x))/x ?
The domain of sqrt(x+5)-(sqrt(3-x))/x is -5<= x<0\lor 0<x<= 3