What is the domain of y=sqrt(x/(x+2))-x/(x-2) ?

The domain of y=sqrt(x/(x+2))-x/(x-2) is x 2

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domain of y=sqrt(x/(x+2))-x/(x-2)

domain

y = \frac{x}{x + 2} - \frac{x}{x - 2}

x < - 2 or 0 \leq x < 2 or x > 2

Interval Notation

Solution steps

Find non-negative values for radicals:

x < - 2 or x \geq 0

Find undefined (singularity) points:

x = - 2, x = 2

Combine real regions and undefined points for final function domain

x < - 2 or 0 \leq x < 2 or x > 2

x^{2} - 6 x - 3

f (x) = \frac{10}{x ^{2} + 1}

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

x^{\frac{1}{5}} (x - 4)

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

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