What is the domain of (x^2-4)/(2x^2-1) ?

The domain of (x^2-4)/(2x^2-1) is x 1/(sqrt(2))

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domain of (x^2-4)/(2x^2-1)

domain

x < - \frac{1}{2} or - \frac{1}{2} < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

x < - \frac{1}{2} or - \frac{1}{2} < x < \frac{1}{2} or x > \frac{1}{2}

What is the domain of (x^2-4)/(2x^2-1) ?
The domain of (x^2-4)/(2x^2-1) is x<-1/(sqrt(2))\lor-1/(sqrt(2))<x< 1/(sqrt(2))\lor x> 1/(sqrt(2))