4MA1/2HR Jun 2018, Question 22: Algebraic Fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Simplify the product of (4x² − 25)/(5x² + 2x − 7) and the difference 2/(x − 3) − 3/(2x − 5), giving one fraction in simplest form.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 4 marks
- 14x² − 25 = (2x + 5)(2x − 5)
- 25x² + 2x − 7 = (5x + 7)(x − 1)
- 32/(x − 3) − 3/(2x − 5) = [2(2x − 5) − 3(x − 3)] / [(x − 3)(2x − 5)]
- 42(2x − 5) − 3(x − 3) = 4x − 10 − 3x + 9 = x − 1
- 5So the bracket is (x − 1) / [(x − 3)(2x − 5)]
- 6The expression is (2x + 5)(2x − 5) / [(5x + 7)(x − 1)] × (x − 1) / [(x − 3)(2x − 5)]
- 7Cancel (2x − 5) and cancel (x − 1)
- 8= (2x + 5) / [(5x + 7)(x − 3)]
Answer(2x+5)/((5x+7)(x-3))
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