Simplifying rational expressions

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That actually works, thanks! And now if I have a power series with coefficients in ring R as in your answer above, is there any way to make sage automatically simplify the coefficients without calling factor() for them? I am computing rather complicated expressions with a lot of steps, so I don't even know at what point I would need to call for it if I had to do it manually

This is an other question.

And in the above answer there is no power series. So if the power series should be really considered over R, make it clear, e.g. instead of ...a power series with coefficients in ring R as in your answer above... better let R be as above, and let us consider a power series with coefficients in R. And give that series explicitly, so we have an example where something was not simplified. What is "it" in so I don't even know at what point I would need to call for it if I had to do it manually ? The factor method? (That we tried to avoid in the previous line.)

Let R be as in answer above (rational functions of x,y and z). Now let's consider R((q)) -formal Laurent series with coefficients in R. My problem is that sage keeps coefficients of those series not simplified (probably it thinks that all rational numbers are units and hence all the same) and also expanded. Now if I multiply two such series the coefficients become even worse (in sage's representation, but I know they can be simplified). So my question is: is there a way to make sage keep automatically simplifying coefficients every time I perform operations on Laurent series? Also I would really prefer if the coefficients were saved in a factored form if possible. Even if I call factor() for coefficients, when I print a series, the coefficients are in the expanded form.