The rearrangement decides which root attracts

Consider the following statements: $S_1$: There exists an $\epsilon >0$ such that $\forall x_0\in (2-\epsilon ,2+\epsilon )$, the iterative sequence defined by $x(n+1)=6/(5-x_n),n=0,1,2,3,\dots$, converges to $2.S_2$: There exists an $\epsilon >0$ such that $\forall x_0\in (3-\epsilon ,3+\epsilon )$, the iterative sequence defined by $x(n+1)=(x_n^2+6)/5,n=0,1,2,3,\dots$, converges to $3.S_3$: There exists an $\epsilon >0$ such that $\forall x_0\in (3-\epsilon ,3+\epsilon )$, the iterative sequence defined by $x(n+1)=(5x_n-6)/x_n,n=0,1,2,3,\dots$, converges to 3. Then which of the following statements are true?