3.7: Area of shaded region $ABC$

The diagram shows part of the curve $y=2-\dfrac{3}{x-1}$ and the straight line $y=\dfrac{3}{2}-\dfrac{1}{3}x$. The curve intersects the $x$-axis at $A$ and the line at $B$. The line intersects the $x$-axis at $C$. Find the area of the shaded region $ABC$, giving your answer in the form $\ln p+q$, where $p$ and $q$ are rational.