I use Modern Mandarin Chinese Grammar Workbook, and I was doing this exercise in which we rewrite the sentences with "是...的" construction. One of the sentences was 他们一九七零年结婚。I wrote "他们是一九七零年结婚的。" But the answer key says "他们是一九七零年结的婚。" Why did they separate the 结婚? Is my sentence incorrect, or is it just an alternative?
The 是...的 construction is used to give a word, phrase or clause special focus and sense of factual certainty, hence its frequent use in past and descriptive sentences as well as with words denoting a specific time, place, manner or quality.
What's inside of 是...的 receives focus; what's outside of it doesn't. The focus falls primarily on the word that immediately follows 是.
的 is placed after the last word in focus. Usually, that's the word at the very end of the sentence, since the 是...的 construction is often applied to the entire predicate or comment. Other times, the construction is closed off earlier, right after the adverb or verb in focus, leaving the verb or object dangling on their own at the end. Any word after 的 is marked off from the part in focus and, as such, is de-emphasised as known or definite information (a bit as if it were a topic, just tagged on at the end).
So you can see why both sentences in your question are equally valid.
To illustrate the difference using a very awkward attempt at translation, let's think of 结婚, which is a separable V+O phrase, as "tie the knot" and let's also imagine that "the knot" can be split off just as easily in English. Your sentence, 他们是一九七零年结婚的, would translate as "they tied the knot in 1970" or "the thing about them is that they tied the knot in 1970", whereas the sentence in your textbook, 他们是一九七零年结的婚, would be somewhat closer to "they tied (it) in 1970, the knot" or "the thing about their knot is that they tied it in 1970".
Translations aside, there's a slight difference in emphasis between the two sentences, but it's a minimal one. Both are best rendered in English as "it's in 1970 that they tied the knot" or simply "they married in 1970".
In short, by inserting 的 in between 结婚, emphasis is placed on some element of the sentence other than than 结婚. In this case, the emphasis is on 一九七零年. It was in 1970 that they married.
If you think about it, it's not hard to see that the key is 的, and not 结婚.
的 being an auxiliary, is central to Chinese grammar. So if something involving 的 feels strange, that probably means you just came across something new in grammar. Since 的 is a character, let's look it up in a dictionary. (Dictionaries are great for studying grammar, too. There are lots of grammar workbooks around, but dictionaries are written by experts with authority.)
（表强调） [used after the predicative verb to emphasize the doer, the time, the place, etc.]
谁说的？ Who said that?
他是昨天发的烧。 It was yesterday that he had a fever.
主任签的字 | 回来坐的飞机 | 他昨天夜里犯的病 | 我在上海念的中学。
现代汉语词典 also says more or less the same thing, but additionally notes that this usage is limited to past actions/events.