What is the domain of (sqrt(3-x))/(sqrt(x-2)) ?

The domain of (sqrt(3-x))/(sqrt(x-2)) is 2<x<= 3

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domain of (sqrt(3-x))/(sqrt(x-2))

domain

\frac{3 - x}{x - 2}

2 < x \leq 3

Interval Notation

(2, 3]

Solution steps

Find non-negative values for radicals:

2 \leq x \leq 3

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

2 < x \leq 3

What is the domain of (sqrt(3-x))/(sqrt(x-2)) ?
The domain of (sqrt(3-x))/(sqrt(x-2)) is 2<x<= 3