TeX source:

x_{n+1}=x_{n}-\frac{\left(x_{n}\right)^{3}-A}{3\left(x_{n}\right)^{2}}=x_{n}-\frac{x_{n}}{3}+\frac{A}{3\left(x_{n}\right)^{2}}=\frac{1}{3}\left\{2 x_{n}+\frac{A}{\left(x_{n}\right)^{2}}\right\}