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2025 EJC P1 Q1

2025 EJC P1 Q1

5 marks

  1. Solve the inequality \[x+1 > \frac{1}{x-1}\] giving your answer in exact form.

    [3]
  2. Hence solve, in exact form, \( \qquad\qquad\qquad\quad\;\; \mathrm{e}^x+1 > \frac{1}{\mathrm{e}^x-1}\)[2]

Solution:

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Answer:(a) \(-\sqrt2<x<1\) or \(x>\sqrt2\). (b) \(x<0\) or \(x>\frac12\ln2\).

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