A quick question - I'm assuming n is a positive integer. Is there any higher limit for n?
First you need to show that any rational solution must be an integer.
I think it is worth taking 1,2,3 as special cases because in that range there are some solutions.
Now rearrange the equation as x^n+x^n-1...+x+1 = 4.
Then note that the LHS is (x^(n+1)-1)/(x-1) (either by using the formula for the sum of a geometric series or remembering how to factorise x^n-1). This is OK because x=1 is
never going to be a solution for n>=4.
Now you should be easily able to show that there can be no solutions for n>=4 by considering the possible values for the LHS at integer values.