10 A curve $C$ has equation $y=a x+b+\frac{a+2 b}{x-1}$, where $a$ and $b$ are real constants such that $a>0, b \neq-\frac{1}{2} a$ and $x \neq 1$.
(a) Given that $C$ has no stationary points, use differentiation to find the relationship between $a$ and $b$.


It is now given that $b=-2 a$.
(b) Sketch $C$ on the axes on page 19 stating the equations of any asymptotes and the coordinates of the points where $C$ crosses the axes.


(c) On the same axes, sketch the graph of $y=a x-a$.


(d) Hence solve the inequality $x-2-\frac{3}{x-1} \leqslant x-1$.