If a plane passes through the points \((-1, k, 0),(2, k,-1)\), \((1,1,2)\) and is parallel to the line \(\frac{x-1}{1}=\…

If a plane passes through the points \((-1, k, 0),(2, k,-1)\), \((1,1,2)\) and is parallel to the line \(\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}\), then the value of \(\frac{k^2+1}{(k-1)(k-2)}\) is