If the last vowel in a stem is ㅏ or ㅗ (except 하) you add ~아 followed by the remainder of the grammatical principle If the last vowel in a stem is anything but ㅏ or ㅗ you add ~어 followed by the remainder of the grammatical principle In case of 지내다, the final vowel does not end in ㅏ or ㅗ, so we need to add “어” plus whatever we are adding. With these complex vowels, it is irrelevant if you merge the addition to the stem. Both forms (merged and non-merged) would be correct. 지내 + 었다 = 지냈다 or 지내었다 For example: 바래 + 었다 = 바랬다 or 바래었다 매다 + 었다 = 맸다 or 매었다 메다 + 었다 = 멨다 or 메었다 For more information, refer to http://www.italki.com/entry/478726

First, 지내았어요 >> 지내었어요. 지냈어요 is just short form of 지내었어요. Because of that, people prefer to use the short form and that is more often used. That's it.