reestablish or re-establish

verb: bring back into original existence, use, function, or position (Example: "Reestablish peace in the region")

When in doubt, find one dicationary you like, and use whatever hyphenation is used in that dictionary.

See http://www.onelook.com/?w=reestablish&ls=a. All show it without the hypen.

The hyphen in this type of situation has fallen into general disuse. I still prefer it in some cases, where my initial reaction to a word causes confusion. In the word 'cooperate', I see 'coop' first, where I would rather see co-operate. Likewise, 'rees' instead of re-establish. Old fashioned I am, perhaps, but then I'm old enough to be so.

The hyphen has long been dropped from words with the prefixes that end in “e” such as “pre,” “re,” “de.” For example: preexistence, preeminent, reestablish, deemphasize. (found this by typing in google search engine "is reestablish hyphenated")

Your example shows all of the entries without the hyphen because that is the way you input the word into the website search bar. If you instead search for "re-establish," different dictionaries are listed which use that spelling version. I will say though that "reestablish" seems more popular.

And the New Yorker either further confuses the issue or just naughtily adds yet another acceptable variant in using, whether affected or archaic, "reëstablish." Oi! What a language!

The hyphen in words like that is often omitted in American English. You can see in an answer here http://english.stackexchange.com/questions/108021/reestablish-vs-re-establish that reestablish is preferred in American English and re-establish is preferred in Bri