Докажите тождество 1/ (y-1) (y-2)+1/ (y-2) (y-3)+1/ (y-3) (y-4)=3/

1/ (y-1) (y-2)+1/ (y-2) (y-3)+1/ (y-3) (y-4)=3/ (y-1) (y-4) ,1/ (y-1) (y-2)+1/ (y-2) (y-3)+1/ (y-3) (y-4)=(y-3) (y-4)+(y-1) (y-4)+(y-1) (y-2) / (y-1) (y-2) (y-3) (y-4)=(y-4) (y-3+y-1)+(y-1) (y-2) / (y-1) (y-2) (y-3) (y-4)=(y-4) (2y-4)+(y-1) (y-2) / (y-1) (y-2) (y-3) (y-4)=(2 (y-4) (y-2)+(y-1) (y-2) / (y-1) (y-2) (y-3) (y-4)=(y-2) (2 (y-4)+y-1) / (y-1) (y-2) (y-3) (y-4)=(2y-8+y-1) / (y-1) (y-3) (y-4)=(3y-9) / (y-1) (y-3) (y-4)=3 (y-3) / (y-1) (y-3) (y-4)=3 / (y-1) (y-4)