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

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

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

domain

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

x < 0 or 0 < x < \frac{1}{2} or \frac{1}{2} < x \leq 1 or x \geq 2

Interval Notation

(- \infty, 0) \cup (0, \frac{1}{2}) \cup (\frac{1}{2}, 1] \cup [2, \infty)

Solution steps

Find non-negative values for radicals:

x \leq 1 or x \geq 2

Find undefined (singularity) points:

x = \frac{1}{2}, x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < \frac{1}{2} or \frac{1}{2} < x \leq 1 or x \geq 2

What is the domain of (sqrt(x^2-3x+2))/(2x^2-x) ?
The domain of (sqrt(x^2-3x+2))/(2x^2-x) is x<0\lor 0<x< 1/2 \lor 1/2 <x<= 1\lor x>= 2