lim[x趋于无穷]{(x^3)*ln[(x+1)/(x-1)]-2x^2}
=lim[x趋于无穷]{(x^2){xln[(x+1)/(x-1)]-2}
=lim[x趋于无穷]{xln[1+2/(x-1)]-2}/[x^(-2)]
=lim[x趋于无穷]{ln[1+2/(x-1)]+x[1+2/(x-1)]^(-1)[-2/(x-1)^2]}/[-2x^(-3)]
=lim[x趋于无穷]{-2x/(x-1)^2[-2x^(-3)]
=2/3极限性质，复合函数求极限，极限符号可以通过表达式。你一点都不笨，只说明你很认真。坚持！