Simplify $\dfrac{3^{n+2} - 9 \cdot 3^{n}}{3 \cdot 3^{n+2}}$.

Simplify $\dfrac{3^{n+2} - 9 \cdot 3^{n}}{3 \cdot 3^{n+2}}$.
  1. $0$
  2. $1$
  3. $3$
  4. $\dfrac{1}{3}$

Solution

Numerator: $3^{n+2} - 9 \cdot 3^{n} = 9 \cdot 3^{n} - 9 \cdot 3^{n} = 0$. So the expression equals $0$.

Asked in: IMO

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