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I want to write an expression in a more simple form. By simple I mean I want the appearance of the expression to be shorter. I have asked a more general form of this question here and I got the answer that I should write the expression coefficients by using Rationalize. The new equation I'm going to simplify is

-((154080 dr^2 e + 12240 dr e l^2 + 204 alpha dr e ro + 
 1296 alpha dr^2 e ro - 7236000 dr^2 e^2 ro + 3 alpha e l^2 ro - 
 172800 dr e^2 l^2 ro - 8550 alpha dr e^2 ro^2 - 
 51840 alpha dr^2 e^2 ro^2 + 124740000 dr^2 e^3 ro^2 - 
 360 alpha e^2 l^2 ro^2 + 486000 dr e^3 l^2 ro^2 + 
 118800 alpha dr e^3 ro^3 + 680400 alpha dr^2 e^3 ro^3 - 
 937980000 dr^2 e^4 ro^3 + 3375 alpha e^3 l^2 ro^3 - 
 546750 alpha dr e^4 ro^4 - 2916000 alpha dr^2 e^4 ro^4 + 
 2624400000 dr^2 e^5 ro^4 + 18720 dr^2 e Sqrt[3 - 30 e ro] - 
 207360 dr^3 e Sqrt[3 - 30 e ro] + 
 2160 dr e l^2 Sqrt[3 - 30 e ro] - 
 282 alpha dr e ro Sqrt[3 - 30 e ro] - 
 432 alpha dr^2 e ro Sqrt[3 - 30 e ro] - 
 367200 dr^2 e^2 ro Sqrt[3 - 30 e ro] + 
 9331200 dr^3 e^2 ro Sqrt[3 - 30 e ro] - 
 18 alpha e l^2 ro Sqrt[3 - 30 e ro] + 
 86400 dr e^2 l^2 ro Sqrt[3 - 30 e ro] + 
 10080 alpha dr e^2 ro^2 Sqrt[3 - 30 e ro] + 
 12960 alpha dr^2 e^2 ro^2 Sqrt[3 - 30 e ro] - 
 1620000 dr^2 e^3 ro^2 Sqrt[3 - 30 e ro] - 
 139968000 dr^3 e^3 ro^2 Sqrt[3 - 30 e ro] + 
 180 alpha e^2 l^2 ro^2 Sqrt[3 - 30 e ro] - 
 1134000 dr e^3 l^2 ro^2 Sqrt[3 - 30 e ro] - 
 112050 alpha dr e^3 ro^3 Sqrt[3 - 30 e ro] - 
 97200 alpha dr^2 e^3 ro^3 Sqrt[3 - 30 e ro] + 
 43740000 dr^2 e^4 ro^3 Sqrt[3 - 30 e ro] + 
 699840000 dr^3 e^4 ro^3 Sqrt[3 - 30 e ro] + 
 364500 alpha dr e^4 ro^4 Sqrt[3 - 30 e ro] + 
 3780000000 dr e v^2 + 562500 alpha e ro v^2 - 
 90450000000 dr e^2 ro v^2 - 30937500 alpha e^2 ro^2 v^2 + 
 506250000000 dr e^3 ro^2 v^2 + 337500000 alpha e^3 ro^3 v^2 + 
 1170000000 dr e Sqrt[3 - 30 e ro] v^2 - 
 5437500 alpha e ro Sqrt[3 - 30 e ro] v^2 - 
 12150000000 dr e^2 ro Sqrt[3 - 30 e ro] v^2 + 
 81562500 alpha e^2 ro^2 Sqrt[3 - 30 e ro] v^2 - 
 81000000000 dr e^3 ro^2 Sqrt[3 - 30 e ro] v^2 - 
 1005000 alpha c v xr + 22650000 alpha c e ro v xr - 
 113625000 alpha c e^2 ro^2 v xr + 
 505000 alpha c Sqrt[3 - 30 e ro] v xr - 
 7650000 alpha c e ro Sqrt[3 - 30 e ro] v xr + 
 1125000 alpha c e^2 ro^2 Sqrt[3 - 30 e ro] v xr + 
 750 I e l Sqrt[-2 + 
   30 e ro] (alpha ro (26 - Sqrt[3 - 30 e ro] + 
       15 e ro (-18 + 5 Sqrt[3 - 30 e ro])) + 
    240 dr (-16 + 3375 e^2 ro^2 - 27 Sqrt[3 - 30 e ro] + 
       15 e ro (-11 + 15 Sqrt[3 - 30 e ro]))) v Cos[
   t] + (-1 + 15 e ro) (12960 dr^2 e (-1 + 15 e ro)^3 + 
    9 dr e (3 alpha ro (1 - 15 e ro)^2 (-1 + Sqrt[3 - 30 e ro]) - 
       20000000 (-8 - 5 Sqrt[3 - 30 e ro] + 
          15 e ro (4 + Sqrt[3 - 30 e ro])) v^2) + 
    5000 alpha v (2250 e^2 ro^2 v + 
       c (201 - 101 Sqrt[3 - 30 e ro]) xr - 
       15 e ro (5 (7 + 3 Sqrt[3 - 30 e ro]) v + 
          c (101 - Sqrt[3 - 30 e ro]) xr))) Cos[
   2 t])/(72 dr e (-1 + 15 e ro) (1 + Sqrt[
   3 - 30 e ro]) (480 dr Sqrt[3 - 30 e ro] (-1 + 15 e ro) - 
   alpha ro (-3 + 30 e ro + Sqrt[3 - 30 e ro]))))

and the coefficients are not decimal. But when I use Simplify, Mathematica can not write it in a shorter form. Could anyone tell me how can I write such an expression in a shorter form?

Explaining the problem more:

(a b c d + a b c Cos[t] + h l x + h)/(a b  c d l)

could be written in the form

     ( d + Cos[t])/(d l) + (l x + 1)h/(a b  c d l) 

I mean this kind of simplification.

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  • $\begingroup$ What kind of simplification do you think is possible? That is, do you have simplification strategy in mind? $\endgroup$ – m_goldberg May 13 '17 at 7:31
  • $\begingroup$ I've added the example to the question @m_goldberg $\endgroup$ – saraloli saraloli May 13 '17 at 8:04
  • $\begingroup$ check FullSimplify[your expression comes here] $\endgroup$ – Ali Hashmi May 13 '17 at 11:44
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This

Simplify[YourExpr//.a_*Sqrt[3-30 e ro]+b_*Sqrt[3-30 e ro]->(a+b)*Sqrt[3-30 e ro]]

reduces the size by 33%.

This still leaves a number of Sqrt[3-30 e ro] which are nested inside other expressions and you might explore whether you could find a way to apply this technique to combine more of those together.

There are many many Sqrt[3-30 e ro] and only a single Sqrt[-2 + 30 e ro]. Is there any chance that might be a single typo?

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