D[x^2/(x^2+(1-x)^2)-x,x]

t=Simplify[%]

N[Solve[t==0,x] [[1]],10]

N[x^2/(x^2+(1-x)^2)-x,10] /. %

N[Solve[t==0,x] [[2]],10]

N[x^2/(x^2+(1-x)^2)-x,10] /. %