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4MA1/1H Jun 2018, Question 15: Algebraic Fractions

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks

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The question, in short

Reduce a power expression with a negative fractional index, then combine two algebraic fractions into one simplified fraction.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Rewrite (256x²⁰ ÷ y⁸) raised to the power −1/4 in its simplest form.

  1. 1A power of ¼ is a fourth root, so take the fourth root of each part
  2. 2⁴√256 = 4, ⁴√(x²⁰) = x⁵ and ⁴√(y⁸) = y²
  3. 3So the bracket is 4x⁵/y²
  4. 4The power of −1 turns it over, giving y²/(4x⁵)

Answery²/(4x⁵)

Part (b) · 3 marks

Combine 1/(9x² − 25) and 1/(6x + 10) into a single fraction, fully simplified.

  1. 19x² − 25 = (3x − 5)(3x + 5) and 6x + 10 = 2(3x + 5)
  2. 2The common denominator is 2(3x − 5)(3x + 5)
  3. 3First fraction becomes 2/(2(3x − 5)(3x + 5))
  4. 4Second fraction becomes (3x − 5)/(2(3x − 5)(3x + 5))
  5. 5Subtracting the tops: 2 − (3x − 5) = 7 − 3x
  6. 6So the answer is (7 − 3x)/(2(3x − 5)(3x + 5))

Answer(7 − 3x)/(2(3x − 5)(3x + 5))

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