Question

Prove that--- 2 30 +2 29 +2 28 / 2 31 +2 30 +2 29 = 7/10

Answer 1

There is a mistake in this question. It should be like:- 2³⁰ + 2²⁹ + 2²⁸/2³¹ + 2³⁰ - 2²⁹. 
Solution:-
(2³⁰ + 2²⁹ + 2²⁸)/(2³¹ + 2³⁰ - 2²⁹)
= 2²⁸(2³⁰/2²⁸ + 2²⁹/2²⁸ + 2²⁸/2²⁸)/2²⁹(2³¹/2²⁹ + 2³⁰/2²⁹ - 2²⁹/2²⁹)
= 2²⁸(2² + 2 + 1)/2²⁹(2² + 2 - 1)
= (4 + 2 +1)/2²⁹⁻²⁸(4 + 2 -1)
7/2(5)
= 7/10  Answer

Answer 2

Answer with Step-by-step explanation:

2³⁰ + 2²⁹ + 2²⁸/2³¹ + 2³⁰ - 2²⁹. 

Solution:-

(2³⁰ + 2²⁹ + 2²⁸)/(2³¹ + 2³⁰ - 2²⁹)

= 2²⁸(2³⁰/2²⁸ + 2²⁹/2²⁸ + 2²⁸/2²⁸)/2²⁹(2³¹/2²⁹ + 2³⁰/2²⁹ - 2²⁹/2²⁹)

= 2²⁸(2² + 2 + 1)/2²⁹(2² + 2 - 1)

= (4 + 2 +1)/2²⁹⁻²⁸(4 + 2 -1)

7/2(5)

= 7/10 = RHS