Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\...
Simplify 3(2n+1)−4(2n−1)2n+1−2n
2n+1
2n-1
4
1/4
Correct answer is C
Start by expanding 3(2n+1)−4(2n−1)2n+1−2n:
3×2n×21−22×2n×2−12n×2−2n
NUMERATOR : 2n ( 31 X 21 - 22 X 2−1 )
--> 2n ( 3 X 2 — 4 X 12 )
--> 2n ( 6 - 2 )
--> 2n (4)
DENOMINATOR : 2n ( 21 - 1 )
--> 2n ( 2 - 1)
--> 2n
: [ 2n ( 4) ] ÷ 2n
= 4
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