NYJC/2021/JC2/Prelim/P1/Q02

(i) On the same axes, sketch the curves with equations $y=\left|\frac{a x-3 a+2}{3-x}\right|$ and $y=\frac{a}{3} x$, where $a>1$, giving the equations of the asymptotes and the coordinates of the points where the curves meet the axes.

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(ii) Hence, solve the inequality $\left|\frac{a x-3 a+2}{3-x}\right|>\frac{a}{3} x$, giving your answer in terms of $a$.

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