4MA1/2H Jun 2022, Question 19: Algebraic Fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 3 marks
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The question, in short
Given a = 14/(3x − 7) and x = 7/(4y − 3), rewrite a as (py + q)/(ry + s) with integers p, q, r, s, in simplest form.
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Solution · 3 marks
- 1Substitute x: a = 14/(21/(4y − 3) − 7)
- 2Multiply top and bottom by (4y − 3): a = 14(4y − 3)/(21 − 7(4y − 3))
- 3Expand: a = (56y − 42)/(42 − 28y)
- 4Divide top and bottom by 14: (4y − 3)/(3 − 2y)
Answer(4y − 3)/(3 − 2y)
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