2025 CJC Promo Q3

2025 CJC Promo Q3

Junior College 1
7 marks

Without using a calculator, solve the inequality \(\frac{x}{x-2}<\frac{3}{(5x+2)(2-x)}\).[3]

Hence, solve the following inequalities.

  1. \(\frac{e^x}{e^x-2}<\frac{3}{(5e^x+2)(2-e^x)}\)[2]
  2. \(\frac{x}{x-4}>\frac{12}{(5x+4)(4-x)}\)[2]

Solution:

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Answer:\(-\dfrac25<x<2\); (a) \(x<\ln2\); (b) \(-\dfrac45<x<4\)

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