I don't really know how to algebraically simplify the top. I tried to do the divide by x trick (since x is the variable with the greatest denominator available.
I'm not really sure how to get the LaTeX going for the multiple fraction bars yet, but it would look like the original problem with lim x->inf sqrt(2+9x^2/x^2) / 5+2x/x. I do the canceling and the top gives me sqrt(11) / 7, which my text doesn't agree with. I know about the conjugate radical trick, but that doesn't seem like an option here. I've attempted to square the top and bottom but I couldn't find a solution there. Is there a simple algebra trick that I can do to get ride of the square root on the top? All I can think know is that both the top and bottom are approaching infinity, but I can't deduce which is going faster (if either one is going father than the other).