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I have browsed the web and found no information. I have two rational polynomials $f1(x,y)$ and $f2(x,y)$. When I perform f1 + f2, I always get two separate functions. However, I would like to combine them into one rational expression. How do I do that?

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closed as off-topic by m_goldberg, Öskå, ubpdqn, Yves Klett, Mr.Wizard Jul 21 '14 at 14:24

This question appears to be off-topic. The users who voted to close gave these specific reasons:

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Use Together. –  Szabolcs Jul 21 '14 at 3:51
Googling for "mathematica combine rational" gives this page which shows this command. –  Szabolcs Jul 21 '14 at 3:52

2 Answers 2

It's really simple. Just use Together.

f1 = 1/x; f2 = x/(x^2 - 1);

f1 + f2
1/x + x/(-1 + x^2)
Together[f1 + f2]
(-1 + 2 x^2)/(x (-1 + x^2))
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Try this:

f1[x_, y_] = (x + y)^5;
f2[x_, y_] := (x - 3 y)^5

Simplify[Expand /@ (f1[x, y] + f2[x, y])]

(*  2 (x^5 - 5 x^4 y + 50 x^3 y^2 - 130 x^2 y^3 + 205 x y^4 - 121 y^5) *)
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