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0580/21 Oct/Nov 2023, Question 20: Algebraic Fractions

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 6 marks

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The question, in short

Simplify two rational expressions into single fractions in simplest form: one algebraic fraction to reduce, and one sum of two fractions to combine.

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Part (a) · 3 marks

Reduce the fraction (10x² − 60x)/(x² − x − 30) to a single fraction in its simplest form.

  1. 110x² − 60x = 10x(x − 6)
  2. 2x² − x − 30 = (x − 6)(x + 5)
  3. 310x(x − 6)/((x − 6)(x + 5)) = 10x/(x + 5)

Answer10x/(x + 5)

Part (b) · 3 marks

Combine 7/(x + 3) + 5/(8x − 1) into a single fraction in its simplest form.

  1. 1Common denominator (x + 3)(8x − 1)
  2. 27(8x − 1) + 5(x + 3) = 56x − 7 + 5x + 15 = 61x + 8
  3. 3= (61x + 8)/((x + 3)(8x − 1))

Answer(61x + 8)/((x + 3)(8x − 1))

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Also searched as: 0580/21/O/N/23 · 0580_w23_qp_21 · 0580 w23 21 · question 20.
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