Using a rational identity to solve an equation

Using a rational identity to solve an equation

Secondary 2
TGM Original Questions
  1. Simplify \(1+\frac1{x-k}\) as a single fraction.
  2. Using (a), solve \(\frac{x-3}{x-4}-\frac{x-6}{x-7}=\frac{x-4}{x-5}-\frac{x-7}{x-8}\).

Solution:

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

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