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

The domain of (x-sqrt(x)(2x^2-5))/(2x^2-5) is 0 sqrt(5/2)

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domain of (x-sqrt(x)(2x^2-5))/(2x^2-5)

domain

\frac{x - x ( 2 x ^{2} - 5 )}{2 x ^{2} - 5}

0 \leq x < \frac{5}{2} or x > \frac{5}{2}

Interval Notation

[0, \frac{5}{2}) \cup (\frac{5}{2}, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = \frac{5}{2}, x = - \frac{5}{2}

Combine real regions and undefined points for final function domain

0 \leq x < \frac{5}{2} or x > \frac{5}{2}

1 + 2 x

8 x

f (x) = 5 x + 7 x - 8

f (x) = 5 x = 40

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