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4MA1/2HR Jun 2024, Question 26: Algebraic Fractions

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

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The question, in short

Simplify the expression 4 − [(3x − 5) ÷ (3x² + x − 10)/(4x − 1)] into one fraction in its simplest form.

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

Solution · 4 marks

  1. 1Factorise 3x² + x − 10 as (3x − 5)(x + 2)
  2. 2Rewrite the expression: 4(3x² + x − 10)/((3x − 5)(x + 2)) − (3x − 5)(4x − 1)/((3x − 5)(x + 2))
  3. 3Combine the fractions: [4(3x² + x − 10) − (3x − 5)(4x − 1)] / ((3x − 5)(x + 2))
  4. 4Expand numerator: 4(3x² + x − 10) = 12x² + 4x − 40
  5. 5Expand (3x − 5)(4x − 1) = 12x² − 3x − 20x + 5 = 12x² − 23x + 5
  6. 6Subtract: (12x² + 4x − 40) − (12x² − 23x + 5) = 12x² + 4x − 40 − 12x² + 23x − 5 = 27x − 45
  7. 7Numerator is 27x − 45 = 9(3x − 5)
  8. 8Denominator is (3x − 5)(x + 2)
  9. 9Cancel (3x − 5): 9(3x − 5)/((3x − 5)(x + 2)) = 9/(x + 2)

Answer9/(x+2)

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