Помогите разделить дробь 4/(y^3-y^2-y+1) на дробь (y/y^2-2y+1-y/y^2-1+2/y+1

[latex]\frac{4}{y^3-y^2-y+1}:(\frac{y}{y^2-2y+1}-\frac{y}{y^2-1}+\frac{2}{y+1})=\\\\=\frac{4}{y^2(y-1)-(y-1)}:(\frac{y}{(y-1)^2}-\frac{y}{(y-1)(y+1)}+\frac{2}{y+1})=\\\\=\frac{4}{(y-1)(y^2-1)}:\frac{y(y+1)-y(y-1)+2(y-1)^2}{(y-1)^2(y+1)}=\\\\=\frac{4}{(y-1)^2(y+1)}\cdot \frac{(y-1)^2(y+1)}{y^2+y-y^2+y+2y^2-4y+2}=\frac{4}{2y^2-2y+2}=\frac{2}{y^2-y+1}[/latex]