What is the domain of (1/(x-4))/(3-1/(x-4)) ?

The domain of (1/(x-4))/(3-1/(x-4)) is x 13/3

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domain of (1/(x-4))/(3-1/(x-4))

domain

\frac{\frac{1}{x - 4}}{3 - \frac{1}{x - 4}}

x < 4 or 4 < x < \frac{13}{3} or x > \frac{13}{3}

Interval Notation

(- \infty, 4) \cup (4, \frac{13}{3}) \cup (\frac{13}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{13}{3}, x = 4

The function domain

x < 4 or 4 < x < \frac{13}{3} or x > \frac{13}{3}

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

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

f (x) = 6 + x^{2}

f (x) = ln (x^{2} - 1) + 2

f (x) = \frac{x + 3}{x ^{2} + 4 x - 5}

What is the domain of (1/(x-4))/(3-1/(x-4)) ?
The domain of (1/(x-4))/(3-1/(x-4)) is x<4\lor 4<x< 13/3 \lor x> 13/3