SymPy cannot rearrange results while solving a system of equations about Stackelberg game

Function f (assume n=3 for simplicity):

There are 3 symbols related to entities, corresponding to x[j](j=1,2,3) respectively. R and c is other symbols, which can be treated like constant for now. I try to diff f w.r.t x[j], and solve the results equations together and get x[j]=g(R,c). However, sympy cannot rearrange or split x[j] from the equation.

Derivatives:

Expected Results:

from sympy import *
import sympy as sym
real_n = 3
x = IndexedBase('x')
j, k, n = symbols('j,k n', cls=Idx)
f = x[j]*Symbol("R")/Sum(x[k],(k,1,real_n))-Symbol("c")*x[j]
equ = diff(f,x[j])

ee = solve([equ.subs(j,1),equ.subs(j,2),equ.subs(j,3)], (x[1],x[2],x[3]))
simplify(ee)

Sympy's result:

{x[1]: (R*Sum(x[k], (k, 1, 3)) - c*Sum(x[k], (k, 1, 3))**2)/(R*Sum(KroneckerDelta(1, k), (k, 1, 3))),
 x[2]: (R*Sum(x[k], (k, 1, 3)) - c*Sum(x[k], (k, 1, 3))**2)/(R*Sum(KroneckerDelta(2, k), (k, 1, 3))),
 x[3]: (R*Sum(x[k], (k, 1, 3)) - c*Sum(x[k], (k, 1, 3))**2)/(R*Sum(KroneckerDelta(3, k), (k, 1, 3)))}

I tried to check if the indexed symbol caused the error, and wrote x[i] as 3 different symbols, but it still didn't work.

from sympy import *

a, b, c = symbols('a b c', cls=Idx)
R = symbols("R")
eq1 = diff(a/(a+b+c)-a*R,a)
eq2 = diff(b/(a+b+c)-b*R,b)
eq3 = diff(c/(a+b+c)-c*R,c)
print(eq1,"\n",eq2,"\n",eq3)
solve([eq1,eq2,eq3], [a,b,c])

Output:

-R + 1/(a + b + c) - a/(a + b + c)**2 
 -R + 1/(a + b + c) - b/(a + b + c)**2 
 -R + 1/(a + b + c) - c/(a + b + c)**2
[]

Is there something wrong with my approach? Is it possible to approach this problem in SymPy from another angle?

Any suggestions for the solution of equations are also most welcome.

You can use doit to expand the summation and then solve:

In [6]: solve([equ.subs(j,1).doit(),equ.subs(j,2).doit(),equ.subs(j,3).doit()], (x[1],x[2],x[3]))
Out[6]: 
⎡⎛         ____          ⎞⎤
⎢⎜        ╱  2           ⎟⎥
⎢⎜R + 3⋅╲╱  R    2⋅R  2⋅R⎟⎥
⎢⎜─────────────, ───, ───⎟⎥
⎣⎝     18⋅c      9⋅c  9⋅c⎠⎦