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Guys, what happens if 'x > 0' not provided. what 'x > 0' means here?

We need it because sqrt(x) is in the expression : x has to be positive or nul to make srqt() existing. Also, if x=0, we have 1/0, impossible for the GMAT context

You solved the problem as if it were an Theorem and you knew where to arrive at the end.

This is an ambiguous question. Thanks for the info

On such question, I try to simplify the expression by:
> factorizing what I can (ie: 1/sqrt(x))
> pulling up from the denominator to the numerator the constants containing sqrt() (Note that it could be to move a sqrt(x) up also)

these kind of questions (i have forgot their real name) were there in my 9th grade and loved to do them back then. Now when i have seen one such question, i dont know what like after 15 years or so, it took me a few moments to figure out what to do.
anyway, the rules that my teacher told us were, 1)always try to get rid of sqrt from the denominators and 2) use a^2-b^2=(a+b)(a-b) formula.
SO by multiplying and dividing the fraction with sqrt2x+sqrtx, we can easily solve the problem.
and yes, the answer is D.