Identity leading to a numerical inequality

Identity leading to a numerical inequality

Secondary 2
4 marks
TGM Original Questions

Core stretch

Assume \(a\ne0,-1,-2\).

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

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

Solution:

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Answer:(a) \(B-A=\dfrac2{a(a+1)(a+2)}\) (b) the stated inequality holds because this difference is positive at \(a=1500\).

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