  Let $\lambda$ and $\mu$ be beta-Jacobi and beta-Laguerre ensembles with joint
density function $f_{\beta, m, a_1, a_2}$ and $f_{\beta, m, a_1}$,
respectively. Here $\beta>0$ and $a_1, a_2$ and $m$ satisfying . $a_1,
a_2>\frac{\beta}{2}(m-1).$ In this paper, we consider the distance between
$2(a_1+a_2)\lambda$ and $\mu$ in terms of total variation distance and
Kullback-Leibler distance. Following the idea in \cite{JM2017}, we are able to
prove that both the two distances go to zero once $a_1m=o(a_2)$ and not so if
$\lim_{a_2\to\infty}a_1m/a_2=\sigma>0.$
