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4MA1/2HR Jun 2022, Question 23: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 3 marks

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The question, in short

Simplify the product of the difference 20/(x² − 36) − 2/(x − 6) and 1/(4 − x) into one fraction in simplest form.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Solution · 3 marks

  1. 120/(x² − 36) = 20/((x − 6)(x + 6))
  2. 22/(x − 6) = 2(x + 6)/((x − 6)(x + 6))
  3. 320/((x − 6)(x + 6)) − 2(x + 6)/((x − 6)(x + 6)) = (20 − 2x − 12)/((x − 6)(x + 6))
  4. 4= (8 − 2x)/((x − 6)(x + 6))
  5. 5Now multiply by 1/(4 − x):
  6. 6(8 − 2x)/((x − 6)(x + 6)) × 1/(4 − x) = (8 − 2x)/((x − 6)(x + 6)(4 − x))
  7. 78 − 2x = 2(4 − x)
  8. 8= 2(4 − x)/((x − 6)(x + 6)(4 − x))
  9. 9Cancel the factor (4 − x)
  10. 10= 2/((x − 6)(x + 6))
  11. 11= 2/(x² − 36)

Answer2/(x² − 36)

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