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9231 P11 - Nov 2017 - Q9 - 12 marks
6360

The curve \(C\) has equation
\(y=\frac{3 x-9}{(x-2)(x+1)}\)
(i) Find the equations of the asymptotes of \(C\).

(ii) Show that there is no point on \(C\) for which \(\frac{1}{3}\lt y\lt 3\).

(iii) Find the coordinates of the turning points of \(C\).

(iv) Sketch \(C\).

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