Can I omit the last part of the sentence to make it cleaner?
The cost of study for domestic students is one-third of the international student's cost of education.
The cost of study for domestic students is one-third of the international student's.
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2 Answers
It is understandable and idiomatic. Some people will say that it is sloppy and informal, and that may matter to you. If you want to avoid repeating "cost of education", and avoiding repetition is usually a good thing, you can do it another way that will not lead to some people objecting:
The cost of study for domestic students is one-third that of international students.
Yes you can, but I would make some other changes as well. It would also sound better to match the noun forms (you have both plural and singular possessive here). You could also use a pronoun like “that” or “what” to stand in for the noun phrase in a comparative construction like this, which might require another verb. And maybe “tuition” is a better (more specific) word than “cost of study”, because that’s probably what you really mean. So something like:
The tuition charged to domestic students is one third (of) that charged to international students.
Or more simply
The tuition is three times more for international students than domestic students.
