Evaluate $\frac{3^{n+1} - 3^n}{3^{n-1}}$
A6CORRECT
B9
C3
D18
GCEFurther MathematicsSurds, Indices and Logarithms2021
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Why the answer is A, and why the others tempt you.
Factor the numerator: 3^n(3 − 1) = 3^n × 2. Dividing by 3^(n−1) gives 3^n × 2 / 3^(n−1) = 3^(n−(n−1)) × 2 = 3¹ × 2 = 6. The key step is factoring 3^n from the numerator before applying index laws.
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