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2026 NYGH P1 Q1

2026 NYGH P1 Q1

IP 4
6 marks
  1. Simplify \(\dfrac{5x-2}{3x^2-x-2}\times\dfrac{2x-2}{25x^2-4}\), leaving your answer as a single fraction.[3]
  2. Given that \(y=\dfrac{3x^2+u}{x^2+y}\), express \(x\) in terms of \(u\) and \(y\).[3]

Solution:

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Answer:(a) \(\dfrac{2}{(3x+2)(5x+2)}\) (b) \(x=\pm\sqrt{\dfrac{u-y^2}{y-3}}\) for \(y\ne3\); if \(y=3,u=9\), any real \(x\).

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