Simplify (frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n})
-
A.
2n+1 -
B.
2n-1 -
C.
4 -
D.
1/4
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)