for which of the values of x are the following expressions defined

Question

square root of x over the square root if x-2

Answer 1

You can see a graph of sqrt(x)/sqrt(x-2) here:

 

http://hwmath.net/solutions/sqtr-x-over-sqrtx-2.jpg

 

to see where the function is defined for x graphically to view Mark H's comments.

Answer 2

Do you mean sqrt (x) / sqrt (x-2)?

 

The top term is defined only if x ≥ 0, and the bottom term only if x ≥ 2

 

Since the second expression includes all possible values of the first expression, it is the dominant constraint

 

So--the original expression is only valid for x ≥ 2