Simplify \(\frac{9*3^{n+1} – 3^{n+2}}{3^{n+1} – 3^{n}}\)
- 3
-
9
- 27
- 81
The correct answer is: B
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