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 \(B=\dfrac a{a+1}-\dfrac{a-1}{a}\).
- Simplify \(B-A\) as a single fraction.[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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