1. The functions $f(x)$ and $g(x)$ are defined by

$\begin{matrix}f(x) & = & (k-1){x}^{2}-(k-2)x-2kx\inℝ\\g(x) & = & (k-1){x}^{2}-3kx+k+1x\inℝ\end{matrix}$

 where $k$ is a non-zero constant and ${k}^{2}\neq1$.

When the curve $y=f(x)$ and the curve $y=g(x)$ are plotted on the same set of coordinate axes, they intersect once only.

Find, in terms of $k$, the $x$-coordinate of the point of intersection.