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Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\...

Simplify 3(2n+1)4(2n1)2n+12n

A.

2n+1

B.

2n-1

C.

4

D.

1/4

Correct answer is C

Start by expanding 3(2n+1)4(2n1)2n+12n:

3×2n×2122×2n×212n×22n

NUMERATOR : 2n (  31 X 21  -  22 X 21 )

--> 2n ( 3 X 2 — 4 X 12 )

--> 2n ( 6 - 2 ) 

--> 2n (4)

DENOMINATOR : 2n ( 21  -  1 )

--> 2n ( 2 - 1)

  --> 2n

 

: [ 2n ( 4) ] ÷ 2n

= 4