KöMaL 2012 B4459

For $x$>1, let $A$($x$) denote the sum of reciprocals of the positive square-free numbers less than $x$, and let $B$($x$) denote the sum of reciprocals of the non-square-free positive numbers less than $x$. Prove that $A$($x$)>$B$($x$).