\input amstex
\def\Q{\bold Q}

$$\split
\lambda^3+2\lambda^2-\lambda-3&=0,\\
\lambda^3+2\lambda^2-\lambda&=3\;\Bigg/\!\cdot\!\frac{1}{3\lambda},\\
\frac{1}{3}\lambda^2+\frac{2}{3}\lambda-\frac{1}{3}&=\frac{1}{\lambda},\\
\frac{1}{3}(\alpha+2)+\frac{2}{3}(\alpha^2-\alpha)-\frac{1}{3}&=\frac{1}{\lambda},\\
\Q[\alpha]\ni\frac{2}{3}\alpha^2-\frac{1}{3}\alpha+\frac{2}{3}&=\frac{1}{\lambda},
\endsplit$$
\bye