Rationalize the expression and simplify

(sqrt(4+h)-2)/(h)

So I'm not even quite sure as to how I should even begin this problem. My textbook provides this answer:

1/(sqrt(4+h)+2)

But I was under the impression that once you rationalize a problem, you are NOT supposed to have radicals in the denominator.

Thanks in advance

If you rationalize the numerator, then it is OK to have a radical in the denominator.

Multiply top and bottom by \(\displaystyle \sqrt{4+h}+2\) and it'll fall into place.

Of course because (sqrt(4+h)-2)/(sqrt(4+h)-2) is still equal to 1 so essentially multiplying by 1 does not change the equation. Wow thanks I really appreciate it right now.
Now time to work this out on my white board

:lol:

thanks once again very much.