RI/2021/JC1/Promo/P1/Q06

(i) On the same axes, sketch the graphs of $y=x+2+\frac{1}{x-1}$ and $y=|2 x+2|$, stating the coordinates of any points of intersections with the axes, turning points and the equations of any asymptotes.

[5]

(ii) Hence solve the inequality
$$x+2+\frac{1}{x-1}>|2 x+2|$$