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JAMB 1984 · UME · Q14

Simplify 3n−3n−133×3n−27×3n−1\dfrac{3^n - 3^{n-1}}{3^3 \times 3^n - 27 \times 3^{n-1}}.

Worked solution (try it first)
  1. Write 333^3 as 27, so the bottom is 27×3n−27×3n−127 \times 3^n - 27 \times 3^{n-1}.
  2. Take out the common factor 27: the bottom is 27(3n−3n−1)27(3^n - 3^{n-1}).
  3. The bracket is the same as the top, so it cancels and leaves 127\frac{1}{27}, option C.

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