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

Explanation

Start by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):

\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\)

NUMERATOR : 2\(^n\) (  3\(^1\) X 2\(^1\)  -  2\(^2\) X 2\(^{-1}\) )

--> 2\(^n\) ( 3 X 2 — 4 X \(\frac{1}{2}\) )

--> 2\(^n\) ( 6 - 2 ) 

--> 2\(^n\) (4)

DENOMINATOR : 2\(^n\) ( 2\(^1\)  -  1 )

--> 2\(^n\) ( 2 - 1)

  --> 2\(^n\)

⇒ \(\frac{2^n ( 4)}{2^n}\)

= 4

There is an explanation video available .