The rearrangement decides which root attracts

Consider the following statements: $S_{1}$: There exists an $\varepsilon > 0$ such that $\forall{}x_{0} \in (2 - \varepsilon, 2 + \varepsilon)$, 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 $\varepsilon > 0$ such that $\forall{}x_{0} \in (3 - \varepsilon, 3 + \varepsilon)$, 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 $\varepsilon > 0$ such that $\forall{}x_{0} \in (3 - \varepsilon, 3 + \varepsilon)$, 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?