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4MA1/1H Jan 2021, Question 12: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Algebra question with two parts: combine two algebraic fractions into one simplified fraction, then expand and simplify a product of three factors.

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Part (a) · 3 marks

Write 4/(x − 2) − 3/(x + 1) as one fraction in simplest form.

  1. 14/(x − 2) − 3/(x + 1) = [4(x + 1) − 3(x − 2)]/((x − 2)(x + 1))
  2. 2Numerator: 4x + 4 − 3x + 6 = x + 10
  3. 3So the single fraction is (x + 10)/((x − 2)(x + 1))

Answer(x + 10)/((x − 2)(x + 1))

Part (b) · 3 marks

Expand and simplify 2x(x − 5)(x − 3).

  1. 12x(x − 5) = 2x² − 10x
  2. 2(2x² − 10x)(x − 3) = 2x³ − 6x² − 10x² + 30x
  3. 3Collect like terms: 2x³ − 16x² + 30x

Answer2x³ − 16x² + 30x

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