4MA1/2H Jun 2024, Question 20: Algebraic Fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Given k = x − y and x = 1/(4y), rewrite 5k/(x + 2) as (a − by²)/(c + dy) with integer a, b, c, d.
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Solution · 3 marks
- 1k = x − y and x = 1/(4y)
- 2So k = 1/(4y) − y
- 35k = 5/(4y) − 5y
- 4x + 2 = 1/(4y) + 2
- 5So 5k/(x + 2) = (5/(4y) − 5y) ÷ (1/(4y) + 2)
- 6Multiply the numerator and the denominator by 4y
- 7Numerator: 4y × (5/(4y) − 5y) = 5 − 20y²
- 8Denominator: 4y × (1/(4y) + 2) = 1 + 8y
- 95k/(x + 2) = (5 − 20y²)/(1 + 8y)
Answer(5 − 20y²)/(1 + 8y)
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