Simplifying fractions with exponents I'm revising for an exam, which I have the solutions to. One of the questions asks me to prove that a sequence is a Cauchy sequence, sequence is written as:
$ a_n = \frac{2^{n+2}+1}{2^n},$
and then in the solutions, it has:
$\left | a_n - a_m \right | = \left | \frac{2^{n+2}+1}{2^n} - \frac{2^{m+2}+1}{2^m} \right | = \left | \frac {1}{2^n} - \frac {1}{2^m} \right |$
I am extremely rusty on my math skills, but could someone explain how the $2^{nd}$ and $3^{rd}$ absolute values are equal?

The important equality is:
$$\frac{2^{n+2} + 1}{2^n} = \frac{2^{n+2}}{2^n} + \frac{1}{2^n} = 2^2 + \frac{1}{2^n}$$
The same process is performed on both fractions and the $2^2$ drops out. (One fraction contributes a $+4$ while the other fraction contributes a $-4$.)
