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9709 P11 - Nov 2016 - Q11
1182

The point \(P(3, 5)\) lies on the curve \(y = \frac{1}{x-1} - \frac{9}{x-5}\).

(i) Find the \(x\)-coordinate of the point where the normal to the curve at \(P\) intersects the \(x\)-axis.

(ii) Find the \(x\)-coordinate of each of the stationary points on the curve and determine the nature of each stationary point, justifying your answers.

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