let $x>0$,and $n$ be postive integers, show that
$$\dfrac{n(x^n+1)}{1+x+x^2+\cdots+x^{n-1}}\le\dfrac{(n+1)(x^{n+1}+1)}{1+x+x^2+\cdots+x^n}$$

My try: it must prove
$$(n+1)(x^{n+1}+1)(1+x+x^2+……+x^{n-1})-n(x^n+1)(1+x+x^2+……+x^n)\ge 0$$
then I fell very hard prove it,maybe can use AM-GM inequality to prove it