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

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

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

domain

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

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

Interval Notation

(- \infty, - 2) \cup [0, 2) \cup (2, \infty)

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

\frac{- 1}{2 5 - x}

f (x) = 1 - \frac{9}{x ^{2}}

f (x) = \frac{x - 7}{x ^{2} + 14 x + 49}

f (x) = x^{4} - 4 x^{3} + \frac{14}{3} x^{2} - \frac{9}{7} x + 2

f (x) = \frac{x - 5}{x + 7}

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