Using a rational identity to solve an equation

Using a rational identity to solve an equation

Secondary 2
4 marks
TGM Original Questions

Core stretch

  1. Simplify \(1+\dfrac1{x-k}\) as a single fraction.[2]
  2. Using (a), solve \(\dfrac{x-3}{x-4}-\dfrac{x-6}{x-7}=\dfrac{x-4}{x-5}-\dfrac{x-7}{x-8}\).[2]

Solution:

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Answer:(a) \(\dfrac{x-k+1}{x-k}\) (b) \(x=6\).

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