No solution
as
x+1/x=1
x+1=x
x=x-1 No real solutions
Use mathway.com/algebra if you want to check.
Thanks guest.
If you mean
\(x+\frac{1}{x}=1\qquad then\\ x^2+1=x\\ x^2-x+1=0\\ x=\frac{1\pm\sqrt{1-4}}{2}\\ x=\frac{1\pm\sqrt{-3}}{2}\\ x=\frac{1\pm\sqrt{3}\;i}{2}\\\)
This is not a real number. So if you are only looking for real numbers then guest is right. There are no solution.