Simplify \(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)
FURTHER MATHEMATICS
WAEC 2022
Simplify \(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)
- A. 3
- B. 9
- C. 27
- D. 81
Correct Answer: B. 9
Explanation
\(\frac{9*3^{n+1} - 3^{n+2}}{3^{n+1} - 3^{n}}\)
= \(\frac{3^n * 3^n * 3^1 * - 3^2 * 3^2}{3^n * 3^1 - 3^n}\)
= \(\frac{3^n (3^2 * 3^1)}{3^n (3^1 - 1)}\)
= \(\frac{27-9}{3-1}\)
= \(\frac{18}{2}\)
= 9
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