What is the domain of (sqrt(2x+7))/(x-|x|) ?

The domain of (sqrt(2x+7))/(x-|x|) is -7/2 <= x<0

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domain of (sqrt(2x+7))/(x-|x|)

domain

- \frac{7}{2} \leq x < 0

Interval Notation

[- \frac{7}{2}, 0)

Solution steps

Find non-negative values for radicals:

x \geq - \frac{7}{2}

Find undefined (singularity) points:

x \geq 0

Combine real regions and undefined points for final function domain

- \frac{7}{2} \leq x < 0

What is the domain of (sqrt(2x+7))/(x-|x|) ?
The domain of (sqrt(2x+7))/(x-|x|) is -7/2 <= x<0