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4MA1/2HR Jan 2023, 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 sum of a product of two algebraic fractions and 29 − 4x into one fraction in its simplest form.

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Solution · 4 marks

  1. 1Factorise: 4x² − 17x − 15 = (4x + 3)(x − 5)
  2. 2Factorise: 2x² − 7x + 3 = (2x − 1)(x − 3)
  3. 3Factorise: x² − 25 = (x + 5)(x − 5)
  4. 4The expression is (4x + 3)(x − 5)/(2x − 1) × (2x − 1)(x − 3)/[(x + 5)(x − 5)] + (29 − 4x)
  5. 5Cancel (2x − 1) and (x − 5) in the product: (4x + 3)(x − 3)/(x + 5) + (29 − 4x)
  6. 6Write over the common denominator (x + 5): [(4x + 3)(x − 3) + (29 − 4x)(x + 5)]/(x + 5)
  7. 7(4x + 3)(x − 3) = 4x² − 9x − 9
  8. 8(29 − 4x)(x + 5) = −4x² + 9x + 145
  9. 9Numerator = 4x² − 9x − 9 − 4x² + 9x + 145 = 136
  10. 10= 136/(x + 5)

Answer136/(x+5)

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