Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\)
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Correct Answer: Option C
Explanation:
Start by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):
\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\)
Solving the equation above gives;
\(\frac{2^n \times 2^1 \times 2}{2^n} = 2 \times 2 = 4\)
Start by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):
\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\)
Solving the equation above gives;
\(\frac{2^n \times 2^1 \times 2}{2^n} = 2 \times 2 = 4\)