The diagram shows part of the curve

\(y=2-\frac{3}{x-1}\)

and the straight line

\(6y=9-2x.\)

The curve intersects the \(x\)-axis at point \(A\), and the line at point \(B\). The line intersects the \(x\)-axis at point \(C\). Find the area of the shaded region \(ABC\), giving your answer in the form

\(p+\ln q,\)

where \(p\) and \(q\) are rational numbers.