What is the domain of f(x)=(x-5)/(2x(3x-5)) ?

The domain of f(x)=(x-5)/(2x(3x-5)) is x 5/3

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domain of f(x)=(x-5)/(2x(3x-5))

domain

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

x < 0 or 0 < x < \frac{5}{3} or x > \frac{5}{3}

Interval Notation

(- \infty, 0) \cup (0, \frac{5}{3}) \cup (\frac{5}{3}, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = \frac{5}{3}

The function domain

x < 0 or 0 < x < \frac{5}{3} or x > \frac{5}{3}

What is the domain of f(x)=(x-5)/(2x(3x-5)) ?
The domain of f(x)=(x-5)/(2x(3x-5)) is x<0\lor 0<x< 5/3 \lor x> 5/3