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How to divide continued fractions in abbreviated notation?

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Sorry, but there is no known simple way to do the basic 4 operations with continued fractions.  They are very useful for revealing approximation properties of real numbers, but they are a *terrible* way to represent numbers for the purpose of making computations with multiple numbers.

If you look online then you can find out about Gosper's algorithm, but I do not believe this is the kind of "nice" process you're hoping exists.

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