Answer
$\dfrac{1}{x^n-4}$
Work Step by Step
The given expression can be written as:
$\\=\dfrac{x^n+4}{(x^n)^2-4^2}$
RECALL:
$a^2-b^2=(a-b)(a+b)$
Factor the denominator using the formula above where $a=x^n$ and $b=4$ to have:
$\\=\dfrac{x^n+4}{(x^n-4)(x^n+4)}$
Cancel the common factors to have:
$\\\require{cancel}=\dfrac{\cancel{x^n+4}}{(x^n-4)\cancel{(x^n+4)}}
\\=\dfrac{1}{x^n-4}$
