What is the value of 2^2014+2^20122^2014-2^2012?

Suppose that x=2^2012. Then the given expression is equal to 4x+x4x-x=5x3x=53.

smc

prealgebra senior

Problem

What is the value of

\frac{2 ^{2014} + 2 ^{2012}}{2 ^{2014} - 2 ^{2012}} ?

(A)

- 1

(B)

1

(C)

\frac{5}{3}

(D)

2013

Solution

Suppose that

x = 2^{2012} .

Then the given expression is equal to

\frac{4 x + x}{4 x - x} = \frac{5 x}{3 x} = \frac{5}{3} .

Final answer