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4MA1/1HR Jun 2023, Question 23: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Simplify the expression (x² − 4) ÷ ((4x² − 7x − 2)/x) − 2x and give the result as ax²/(bx + c) with integer a, b, c.

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

Solution · 4 marks

  1. 1x² − 4 = (x + 2)(x − 2)
  2. 24x² − 7x − 2 = (4x + 1)(x − 2)
  3. 3Expression is: x(x² − 4) / (4x² − 7x − 2)
  4. 4Substitute factorised forms: x(x + 2)(x − 2) / ((4x + 1)(x − 2))
  5. 5Cancel (x − 2): x(x + 2) / (4x + 1)
  6. 6Expand numerator: (x² + 2x) / (4x + 1)
  7. 7Now subtract 2x: (x² + 2x)/(4x + 1) − 2x
  8. 8Write 2x as fraction: 2x(4x + 1)/(4x + 1) = (8x² + 2x)/(4x + 1)
  9. 9Subtract: (x² + 2x − 8x² − 2x)/(4x + 1)
  10. 10Simplify numerator: (−7x²)/(4x + 1)
  11. 11−7x²/(4x + 1)

Answer−7x²/(4x+1)

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