What is the domain of (8(6/(5x-4))+4)/(x-4) ?

The domain of (8(6/(5x-4))+4)/(x-4) is x 4

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domain of (8(6/(5x-4))+4)/(x-4)

domain

\frac{8 ( \frac{6}{5 x - 4} ) + 4}{x - 4}

x < \frac{4}{5} or \frac{4}{5} < x < 4 or x > 4

Interval Notation

(- \infty, \frac{4}{5}) \cup (\frac{4}{5}, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

x = 4, x = \frac{4}{5}

The function domain

x < \frac{4}{5} or \frac{4}{5} < x < 4 or x > 4

What is the domain of (8(6/(5x-4))+4)/(x-4) ?
The domain of (8(6/(5x-4))+4)/(x-4) is x< 4/5 \lor 4/5 <x<4\lor x>4