What is the domain of sqrt((x+2)/(3x-5)) ?

The domain of sqrt((x+2)/(3x-5)) is x 5/3

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domain of sqrt((x+2)/(3x-5))

domain

\frac{x + 2}{3 x - 5}

x \leq - 2 or x > \frac{5}{3}

Interval Notation

(- \infty, - 2] \cup (\frac{5}{3}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 2 or x > \frac{5}{3}

Find undefined (singularity) points:

x = \frac{5}{3}

Combine real regions and undefined points for final function domain

x \leq - 2 or x > \frac{5}{3}

f (x) = x - \frac{5}{g ( x )} (x) = x + 6

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

9 - x

f (x) = \frac{1}{17 - t}

x + 3 - 1

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