sqrt\left(\frac{\left(8x-5\right?}{\left(x-3\right?}\right?

This was an exam question. Is it always that we sketch the rational function and delete the part that goes below the X axis and determine the domain and range?

Does it always work that way?

I saw on the internet that this has complex roots. Is there something that I am missing here?

How do I sketch such graphs? How do I know the domain and range algebraically?