-4/(y^4+1)-2/(y^2+1)-1/(y+1)+1/(y-1)=2y/(-1+y^8)解方程

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-4/(y^4+1)-2/(y^2+1)-1/(y+1)+1/(y-1)=2y/(-1+y^8)解方程
-4/(y^4+1)-2/(y^2+1)-1/(y+1)+1/(y-1)=2y/(-1+y^8)
解方程

-4/(y^4+1)-2/(y^2+1)-1/(y+1)+1/(y-1)=2y/(-1+y^8)解方程
原方程左边=-4/(y^4+1) -2/(y^2+1) +[1/(y-1) -1/(y+1)]
=-4/(y^4+1) -2/(y^2+1) +[(y+1)-(y-1)]/[(y-1)*(y+1)]
=-4/(y^4+1) -2/(y^2+1) +2/(y^2-1)
=-4/(y^4+1) +2[1/(y^2-1) -1/(y^2+1)]
=-4/(y^4+1) +2[(y^2+1)-(y^2-1)]/[(y^2+1)*(y^2-1)]
=-4/(y^4+1) +4/(y^4-1)
=4[1/(y^4-1) -1/(y^4+1)]
=4[(y^4+1)-(y^4-1)]/[(y^4-1)*(y^4+1)]
=8/(y^8-1)
原方程右边=2y/(-1+y^8)
所以 2y=8
所以 y=4