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WAEC 2022 · Paper 1 · Q4

Simplify: 9×3n+1−3n+23n+1−3n\dfrac{9 \times 3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}.

Worked solution (try it first)
  1. Write each term as a multiple of 3n3^n: 9×3n+1=27×3n9 \times 3^{n+1} = 27 \times 3^n, 3n+2=9×3n3^{n+2} = 9 \times 3^n and 3n+1=3×3n3^{n+1} = 3 \times 3^n.
  2. Take out 3n3^n: the top is 3n(27−9)=18×3n3^n(27 - 9) = 18 \times 3^n and the bottom is 3n(3−1)=2×3n3^n(3 - 1) = 2 \times 3^n.
  3. Cancel 3n3^n: 182=9\dfrac{18}{2} = 9, option B.

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