In your first step, when you bring 1/x under the radicals, it needs to be 1/x^2.
Oh, I'm still a little confused. Our professor just told us to divide out each term by a common factor or factor some common factor out of each term, so that's just what I did. I didn't think it mattered what kind of term it was but apparently it's something very different.
So you multiply every term by (1/x) every time?
In your first method, how did your 1/x become sqrt(1/x^2)?
another approach:
we may assume x > 2, since we are taking the limit at "positive infinity".
thus:
, and
so:
and:
since:
(it's always (for x > 2) bigger than half the square root of x+2, right?)