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It seems that FullSimplify is not working here. I want to arrange the expression in ascending powers of x

    FullSimplify[(
  24 (15 + 4 Sqrt[3] x - 4 x^2 + x^4))/((3 + Sqrt[3] x)^4 (29 - 
     2 x^2 + x^4)) + (
  64 (58 + 165 x^2 + 28 x^4 + x^6))/(-87 + 35 x^2 - 5 x^4 + x^6)^2]
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  • $\begingroup$ Generally, FullSimplify does not arrange expressions in some way, but only rewrites the expression in a more simple form. However, it is not clear what do you need in this expression. Indeed, you have two fractions. So, your question can be interpreted in several ways. Could you give a simple example from which it is clear what are you after? $\endgroup$ Jul 4 at 11:33
  • $\begingroup$ You are probably looking for either Expand or Collect: Expand[FullSimplify[(24 (15 + 4 Sqrt[3] x - 4 x^2 + x^4))/((3 + Sqrt[3] x)^4 (29 - 2 x^2 + x^4)) + (64 (58 + 165 x^2 + 28 x^4 + x^6))/(-87 + 35 x^2 - 5 x^4 + x^6)^2]] $\endgroup$
    – Domen
    Jul 4 at 12:11
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Not sure this is what you want, but here is a way to bring it into a simple form:

a = (24 (15 + 4 Sqrt[3] x - 4 x^2 + x^4))/((3 + Sqrt[3] x)^4 (29 - 
       2 x^2 + x^4)) + (64 (58 + 165 x^2 + 28 x^4 + x^6))/(-87 + 
      35 x^2 - 5 x^4 + x^6)^2

b = Denominator[a[[2]]]
c = Numerator[a[[2]]]
d = a[[1]] + c/Factor[b]
e = Together[d]
f = Numerator[e]
g = Denominator[e]
h = Factor[f, Extension -> Sqrt[3]]/g // Simplify

$$\frac{8 \left(x^8-4 \sqrt{3} x^7+42 x^6-8 \sqrt{3} x^5+676 x^4-84 \sqrt{3} x^3+4510 x^2-464 \sqrt{3} x+1827\right)}{3 \left(x^2-3\right)^2 \left(x^4-2 x^2+29\right)^2}$$

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