# How to write an expression in shorter form

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.

• What kind of simplification do you think is possible? That is, do you have simplification strategy in mind? Commented May 13, 2017 at 7:31
• I've added the example to the question @m_goldberg Commented May 13, 2017 at 8:04
• check FullSimplify[your expression comes here] Commented May 13, 2017 at 11:44

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