2015 AJC P1 Q1

2015 AJC P1 Q1

6 marks

Prelims

Without using a graphic calculator, solve the inequality \(\frac{x+2}{2x-1}<2x+1\).[3]

Hence find the exact solution of the inequality \(\frac{2{{x}^{2}}+1}{2-{{x}^{2}}}<\frac{2+{{x}^{2}}}{{{x}^{2}}}\).[3]

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Answer:\(x < -\sqrt 2 \) or \(x > \sqrt 2\) or \(-1 < x < 0\) or \(0 < x < 1\)

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