Answer
$2x^{n+1}+4x$
Work Step by Step
Factor the numerators and the denominators, when needed to have:
$\\=\dfrac{(x^n+2)(x^n+2)}{4x-3} \cdot \dfrac{2x(4x-3)}{x^n+2}$
Cancel the common factors to have:
$\\\require{cancel}=\dfrac{\cancel{(x^n+2)}(x^n+2)}{\cancel{4x-3}} \cdot \dfrac{2x\cancel{(4x-3)}}{\cancel{x^n+2}}
\\=(x^n+2)(2x)
\\=2x^{n+1}+4x$
