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4MA1/1H Jun 2022, Question 11: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Rewrite 9x² − 4y² as a product of two brackets, then combine 7/8 and (x + 3)/(4x) into one simplified fraction.

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

Part (a) · 2 marks

Write 9x² − 4y² as a product of two bracketed factors.

  1. 19x² = (3x)² and 4y² = (2y)², so this is a difference of two squares
  2. 2So 9x² − 4y² = (3x + 2y)(3x − 2y)

Answer(3x + 2y)(3x − 2y)

Part (b) · 3 marks

Combine 7/8 and (x + 3)/(4x) into one fraction, reduced to its simplest form.

  1. 1The common denominator of 8 and 4x is 8x
  2. 27/8 = 7x/(8x) and (x + 3)/(4x) = 2(x + 3)/(8x)
  3. 3So the expression is (7x − 2(x + 3))/(8x)
  4. 4Expand the top: 7x − 2x − 6 = 5x − 6
  5. 5So the answer is (5x − 6)/(8x)

Answer(5x − 6)/(8x)

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