4MA1/2H Jan 2020, Question 24: Algebraic Fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 4 marks
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The question, in short
Simplify the quotient of two rational expressions into one fraction, combining 4/(2x − 5) − 3/(2x − 3) and dividing by (9x − 4x³)/(6x² − 17x + 5).
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Solution · 4 marks
- 1First bracket: [4(2x − 3) − 3(2x − 5)] / ((2x − 5)(2x − 3)) = (2x + 3)/((2x − 5)(2x − 3))
- 2Factorise: 9x − 4x³ = x(3 − 2x)(3 + 2x) and 6x² − 17x + 5 = (3x − 1)(2x − 5)
- 3Divide by multiplying by the flipped fraction: (2x + 3)(3x − 1)(2x − 5) / ((2x − 5)(2x − 3) x(3 − 2x)(3 + 2x))
- 4Cancel (2x − 5) and (2x + 3): (3x − 1)/(x(2x − 3)(3 − 2x))
Answer(3x − 1)/(x(2x − 3)(3 − 2x))
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