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4024/11 Oct/Nov 2021, Question 23: Algebraic Fractions

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Two algebra tasks: multiply out and simplify the product of two binomials, then combine two algebraic fractions over different denominators into one simplified fraction.

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Part (a) · 2 marks

Multiply out the brackets for (x + 5)(x − 2) and collect like terms to give the simplified expansion.

  1. 1(x + 5)(x − 2) = x² − 2x + 5x − 10
  2. 2= x² + 3x − 10

Answerx² + 3x − 10

Part (b) · 3 marks

Combine 3/(x − 4) and 2/(x + 5) into one fraction, then simplify the result.

  1. 1Common denominator (x − 4)(x + 5)
  2. 23(x + 5) + 2(x − 4) = 3x + 15 + 2x − 8 = 5x + 7
  3. 3= (5x + 7)/((x + 5)(x − 4))

Answer(5x + 7)/((x + 5)(x − 4)) or (5x + 7)/(x² + x − 20)

Stuck on a step? Read the free lesson: Algebraic Fractions

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