Why do we conclude that answer or x should only be positive?
I am asking from the algebraic perspective if x= 1/(3+x) then id x is negative the expression still holds.
Because every individual term in the expression is positive (1+3/1+3/1+3/1+…). For x = 1/(3+x) there will probably be two solutions, one positive and one negative (it is a quadratic after all). But the expression given, consisting as it does entirely of positive quantities, cannot yield a negative result.
CAT-holics 
Nice method to solve it
sir how 2 approach for square root of 4+ square root of 4 -square root of 4 and so on till infinity..
Why do we conclude that answer or x should only be positive?
I am asking from the algebraic perspective if x= 1/(3+x) then id x is negative the expression still holds.
Because every individual term in the expression is positive (1+3/1+3/1+3/1+…). For x = 1/(3+x) there will probably be two solutions, one positive and one negative (it is a quadratic after all). But the expression given, consisting as it does entirely of positive quantities, cannot yield a negative result.
regards
J
Thanks was looking for this explanation.