4MA1/1H Jun 2020, Question 21: Algebraic Fractions
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Simplify the expression 1/(3x − 2) × (9x² − 4)/(3x² − 13x − 10) − 7/(x − 1) into one fraction in its simplest form.
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Solution · 5 marks
- 19x² − 4 = (3x + 2)(3x − 2)
- 23x² − 13x − 10 = (3x + 2)(x − 5)
- 3So 1/(3x − 2) × (3x − 2)/(x − 5) = 1/(x − 5)
- 41/(x − 5) − 7/(x − 1) = (x − 1 − 7(x − 5))/((x − 5)(x − 1))
- 5Top: x − 1 − 7x + 35 = 34 − 6x, giving (34 − 6x)/((x − 5)(x − 1))
Answer(34 − 6x)/((x − 5)(x − 1))
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