4MA1/2H Jun 2025, Question 23: Algebraic fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Given that (4x² − 4x − 120)/(5x² − 180) ÷ (x² + 5x)/(10x² + 60x) = p, where p is an integer, find p.
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Solution · 4 marks
- 14x² − 4x − 120 = 4(x − 6)(x + 5)
- 25x² − 180 = 5(x − 6)(x + 6)
- 3x² + 5x = x(x + 5) and 10x² + 60x = 10x(x + 6)
- 4Invert: 4(x − 6)(x + 5)/(5(x − 6)(x + 6)) × 10x(x + 6)/(x(x + 5))
- 5Cancel common factors: 40/5
- 6p = 8
Answer8
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