Trouble centering align*

You have an improper & in the last line of the second alignment, which sets up a second set of alignments; those columns are empty, but the space between the first and the second set is accounted for.

You also have trailing \\ that should be removed.

Original

\documentclass{article} \usepackage{amsmath} \usepackage{showframe} % just for the example \begin{document} words \begin{align*} 1&=ak_1+bl_1\\ n&=n(ak_1+bl_1)\\ &=nak_1+nbl_1\\ &=ak_n+bl_n\\ \end{align*} words \begin{align*} n&=ak_n+bl_n\\ &=ak_n+abx+bl_n-abx\\ &=a(k_n+bx)+b(l_n-ax)\\ &=ar+bs&\\ \end{align*} more words \end{document} 

Fixed version

\documentclass{article} \usepackage{amsmath} \usepackage{showframe} % just for the example \begin{document} words \begin{align*} 1&=ak_1+bl_1\\ n&=n(ak_1+bl_1)\\ &=nak_1+nbl_1\\ &=ak_n+bl_n \end{align*} words \begin{align*} n&=ak_n+bl_n\\ &=ak_n+abx+bl_n-abx\\ &=a(k_n+bx)+b(l_n-ax)\\ &=ar+bs \end{align*} more words \end{document} 

Note

The frame is just for demonstration purposes. Don't load the showframe package yourself.

A mentioned in my comment, the last line in your aligned equations have surplus \\- Also in secon groupu of equations is one ampersund to much ... Try

\documentclass{article} \usepackage{mathtools} \usepackage{lipsum} \begin{document} \lipsum[2] \begin{align*} 1 & = ak_1+bl_1 \\ n & = n(ak_1+bl_1) \\ & = nak_1+nbl_1 \\ & = ak_n+bl_n \end{align*} \lipsum[2] \begin{align*} n & = ak_n+bl_n \\ & = ak_n+abx+bl_n-abx \\ & = a(k_n+bx)+b(l_n-ax) \\ & = ar+bs \end{align*} \lipsum[2] \end{document}