Lemmara logoLemmaraWorked solution

0580/22 May/Jun 2025, Question 19: Algebraic Fractions

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 7 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Simplify three algebraic fraction expressions, writing each as one fraction in its simplest form.

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

Part (a) · 2 marks

Multiply 5a over 6 by 3b over a and simplify to a single fraction.

  1. 1(5a)/6 × (3b)/a = 15ab/(6a)
  2. 2= (5b)/2

Answer(5b)/2

Part (b) · 2 marks

Add p over 2 and 3t over 4, giving one simplified fraction.

  1. 1p/2 = 2p/4
  2. 22p/4 + 3t/4 = (2p + 3t)/4

Answer(2p + 3t)/4

Part (c) · 3 marks

Subtract 3 over x + 1 from 2 over x − 2 as a single simplified fraction.

  1. 1[2(x + 1) − 3(x − 2)]/((x − 2)(x + 1))
  2. 2= (2x + 2 − 3x + 6)/((x − 2)(x + 1))
  3. 3= (8 − x)/((x − 2)(x + 1))

Answer(8 − x)/((x − 2)(x + 1)) or (8 − x)/(x² − x − 2)

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

Practise more algebraic fractions questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on algebraic fractions

Also searched as: 0580/22/M/J/25 · 0580_s25_qp_22 · 0580 s25 22 · question 19.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.