What is the domain of f(x)=(x/(x+5))/(x/(x+5)+5) ?

The domain of f(x)=(x/(x+5))/(x/(x+5)+5) is x -25/6

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domain of f(x)=(x/(x+5))/(x/(x+5)+5)

domain

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

x < - 5 or - 5 < x < - \frac{25}{6} or x > - \frac{25}{6}

Interval Notation

(- \infty, - 5) \cup (- 5, - \frac{25}{6}) \cup (- \frac{25}{6}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{25}{6}, x = - 5

The function domain

x < - 5 or - 5 < x < - \frac{25}{6} or x > - \frac{25}{6}

f (x) = \frac{- 1}{2} (x + 3)

f (x) = - x + 5 - 2

f (x) = \frac{1}{3 - 2 x}

\frac{x + 1}{x}

f (x) = ∣ x ∣ + x^{2}

What is the domain of f(x)=(x/(x+5))/(x/(x+5)+5) ?
The domain of f(x)=(x/(x+5))/(x/(x+5)+5) is x<-5\lor-5<x<-25/6 \lor x>-25/6