simplify (4 x 2^x) - (4 x 2^x-2 ) / (2^x) - (2^ x-1) What would this equation be classified as and what principles do you use for solving?

Question

Simplify

 

4 x 2^x  - 4 x 2^x-2  / 2^x - 2^x-1  

 

Answer 1

4x2^x - 4x2^x-2/2^x - 2^x-1 = 4x(2^x - 2^x-2)/[2^x-1(2 - 1)] = 4x2^x-2(2² - 1)/2^{x- 1} = 3x2^x/2^x-1 = 6x

 

The steps all use algebraic operations including the laws of exponents.