这个分式运算好复杂啊,可以简单点吗?

(x+1)/x(x-1)-(2x+1)/(x^2-1)-(x+2)/(x-1)^2
=(x+1)/x(x-1)-(2x+1)/[(x+1)(x-1)]-(x+2)/(x-1)^2
=[(x+1)^2-(2x+1)x]/[x(x+1)(x-1)]-(x+2)/(x-1)^2
=(x^2+2x+1-2x^2-x)/[x(x+1)(x-1)]-(x+2)/(x-1)^2
=(-x^2+x+1)/[x(x+1)(x-1)]-(x+2)/(x-1)^2
=(-x^2+x+1)(x-1)/[x(x+1)(x-1)^2]-x(x+1)(x+2)/[x(x+1)(x-1)^2]
=[-x^3+x^2+x^2-x+x-1-x(x^2+3x+2)]/[x(x+1)(x-1)^2]
=[-x^3+2x^2-1-x^3-3x^2-2x]/[x(x+1)(x-1)^2]
=-(2x^3+x^2+2x+1)/[x(x+1)(x-1)^2]
=[2x(x^2+1)+(x^2+1)]/[x(x+1)(x-1)^2]
=(2x+1)(x^2+1)/[x(x+1)(x-1)^2]

注：真的是太复杂了，我写得很详细，目的是让楼主看得更清楚一些！！！