6分之5-12分之7+20分之9-30分之11+42分之13-56分之15+72分之17简便方法脱式

原式
=(2+3)/[2*3]+(3+4)/[3*4]+……+(8+9)/[8*9]
=(1/2+1/3)+(1/3+1/4)+……+(1/8+1/9)
=1/2 + 2/3 + 2/4 + 2/5 + 2/6 + 2/7 + 2/8 + 1/9
=1/2 + 2/3 + 1/2 + 2/5 + 1/3 +2/7 + 1/4 + 1/9
= 1+1 + 1/4 + 2/5+ 2/7 + 1/9
= 2+ 13/20 + 25/63
= 2+ 869/1260
= 2又869/1260