limits with fractions (x in denominator)

Hey guys, I'm new here, looked for a thread on this and didn't see any...

So, my problem is that I have to find the limit as h approaches 0 of 8/x^2.

I can get to lim h approaches 0 of [8/(x^2+2xh+h^2)-8/x^2]/h and then I get stuck.

I've been working on this problem for well over an hour now, and I can't seem to figure out what I'm doing wrong. I've tried a ton of different possibilities from there, but I always end up with an h in the denominator somewhere in the limit... Any suggestions on how I can get the h out of the denominator so I can solve this? (Sorry for the terrible formatting, I don't know how to make it look better).

find the derivative or the limit of the function?

Are you finding the derivative or the limit of the function? It looks like you are computing f'(x) using the definition, so I'll go with that....

, multiplying the top and bottom by the common denominator

This then equals

, dividing out an h: