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Show correct output of polynomial

Hi, I am new to sage and I am trying to construct a polynomial to try to transform it. However, when writing it I am getting an incorrect output.

x=var("x") s = (x^2+2x+1) + 1/(x^2+2x+1)

And this is the output I am getting -

x^2+2x + 1/x^2+2x+1 +1 (I am unsure why the 1 is carrying over all the way to right side)

I am looking to obtain the following output to begin transforming it -

x^2+2x+1 + 1/x^2+2x+1

Appreciate any help!