Expectation comparison of order statistics

Question

$n$ variables $X_1,..., X_n$ are independently and identically drawn from pdf $f(x)$ and cdf $F(x)$ on the interval $[\underline{x}, \bar{x}]$. Denote $X_{(i)}$ as the $i$th smallest of all $X_i,i=1,...,n$. $\Bbb{E}$ is the expectation operator and $0<a<1/\bar{x}$ is a given constant. Then what's the sign of $\frac{\Bbb{E}[X_{(2)}-aX_{(2)}^2]}{\Bbb{E}[{(1-aX_{(2)})}^2]}-\frac{\Bbb{E}[X_{(3)}-aX_{(3)}^2]}{\Bbb{E}[{(1-aX_{(3)})}^2]}$?