Identity leading to a numerical inequality

Identity leading to a numerical inequality

Secondary 2
TGM Original Questions

Let \(A=\frac{a+1}{a+2}-\frac a{a+1}\) and \(B=\frac a{a+1}-\frac{a-1}{a}\).

  1. Simplify \(B-A\) as a single fraction.
  2. Hence deduce that \(\frac{1500}{1501}-\frac{1499}{1500}>\frac{1501}{1502}-\frac{1500}{1501}\).

Solution:

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Answer:(a) \(B-A=\frac2{a(a+1)(a+2)}\); (b) the stated inequality holds because this difference is positive at \(a=1500\).

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