Question

Evaluate:

`(2^(n + 2) + 2^n)/(2^(n + 2) - 2^(n + 1))`

Answer 1

Given expression is `(2^(n + 2) + 2^n)/(2^(n + 2) - 2^(n + 1))`,

Using the laws of exponents that is `a^(n + m) = a^n xx a^m` we get,

= `(2^n xx 2^2 + 2^n)/(2^n xx 2^2 - 2^n xx 2^1)`

Now, taking out the common term and simplifying the expression by cancelling out the same term we get,

= `(2^n xx 2^2 + 1)/(2^n xx (2^2 - 2))`

= `(2^2 + 1)/(2^2 - 2)`

= `(4 + 1)/(4 - 2)`

= `5/2`

Therefore, the value of `(2^(n + 2) + 2^n)/(2^(n + 2) - 2^(n + 1)) = 5/2`.