Improper integral

1. The problem statement, all variables and given/known data
integral from 2 to infinty 1/(x-sqrt(x))
3. The attempt at a solution
my teacher wants us to compare it to another function in the form 1/x^p
and not integrate it so
would i compare it to 1/x and then do the limit comparison test
limit as x approaches infinity
i came out with a finite number and since 1/x divegres therefore 1/(x-sqrt(x)) diverges
is this correct.

 

so you are saying since it is larger than something that diverges then it to will diverge.
i see.