I have the irreducible fraction: $$\frac{t^2}{t^4+1}$$ When I use the function "apart" in mathematica the output is $\frac{t^2}{t^4+1}$, which means that it was not able to find a way to factor the denominator, instead when I use "apart" in wolfram alpha, I get $$-\frac{t}{2\sqrt2(-t^2+\sqrt2t-1)}-\frac{t}{2\sqrt2(t^2+\sqrt2t+1)}$$ which is correct. Does anyone know how or why the "apart" function gives different results in mathematica and wolfra alpha (i am strictly talking about irreducible fractions)

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    $\begingroup$ Hi user372003 It is not my intention to criticize but please do not accept the answer I provided for a period of 24 hours. This gives others the chance and impetus to answer. I have never taken back an accepted answer so I do not even know if it is possible but if you can I will not be offended. $\endgroup$
    – bobbym
    Feb 12, 2017 at 10:31
  • $\begingroup$ @bobbym I'll keep in mind for next time! However, the answer you gave me, was the on I was looking for $\endgroup$
    – user372003
    Feb 14, 2017 at 7:40

1 Answer 1


Maybe Alpha is calling additional commands behind the scene.

Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]]

will break it apart but not exactly as you have.

To do better

Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]]//Apart

as Bob Hanlon points out below.

  • $\begingroup$ Thank you! That might have been the problem $\endgroup$
    – user372003
    Feb 12, 2017 at 8:54
  • $\begingroup$ Let us wait for more users to answer and then we will see. $\endgroup$
    – bobbym
    Feb 12, 2017 at 8:54
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    $\begingroup$ Factor[t^2/(t^4 + 1), Extension -> Sqrt[2]] // Apart $\endgroup$
    – Bob Hanlon
    Feb 12, 2017 at 14:06

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