\(y=\frac{t^2-t-1}{t-2}=\frac{t^2-t-1}{t-2}+\frac{1}{3}-\frac{1}{3}=\frac{3t^2-2t-5}{3\left(t-2\right)}-\frac{1}{3}=\frac{\left(t+1\right)\left(3t-5\right)}{3\left(t-2\right)}-\frac{1}{3}\)
\(=\frac{\left(t+1\right)\left(5-3t\right)}{3\left(2-t\right)}-\frac{1}{3}\ge-\frac{1}{3}\)
\(y_{min}=-\frac{1}{3}\) khi \(t=-1\)