$\frac{{9n - 1}}{{4n - 1}} = \frac{{4n - 1 + 5n}}{{4n - 1}} = 1 + \frac{{5n}}{{4n - 1}} = 1 + \frac{5}{{4 - \frac{1}{n}}} \Rightarrow 4 - \frac{1}{n} \in \left\{ { - 1,1, - 5,5} \right\}$