\documentclass{style}
\usepackage{amsmath}
\begin{document}
\begin{gather*}
	f(x) = x^k - s \\
	f'(x) = kx^{k - 1}
\end{gather*}

\begin{gather*}
	x_{n + 1} = x_n - \frac{x_n^k - s}{kx_n^{k - 1}} = \frac{x_n(k - 1) + sx_n^{1 - k}}{k}
\end{gather*}
\end{document}
