简算 7/12-9/20+11/30-13/42+15/56-17/72

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简算 7/12-9/20+11/30-13/42+15/56-17/72

简算 7/12-9/20+11/30-13/42+15/56-17/72
简算 7/12-9/20+11/30-13/42+15/56-17/72

简算 7/12-9/20+11/30-13/42+15/56-17/72
7/12-9/20+11/30-13/42+15/56-17/72
=1/3+1/4-(1/4+1/5)+(1/5+1/6)-(1/6+1/7)+(1/7+1/8)-(1/8+1/9)
=1/3-1/9
=2/9
ps:以后提问不要出现“快!”之类的催促性的话,这是很不友好的!好歹也要说“我很急”这样子谦虚点的话吧

=7/12-17/72+15/56-13/42+11/30-9/20
=42/72-17/72+1/14(15/4-13/3)+1/10(11/3-9/2)
=25/72-1/14*7/12-1/10*5/6 通分,最小公倍数为72*35
=25*35/72*25-7*15/14*12*15-5*60/10*6*60
=97/360

7/12-9/20+11/30-13/42+15/56-17/72
=7/(3*4)-9/(4*5)+11/(5*6)-13/(6*7)+15/ (7*8)-17/(8*9)
=(7/3-7/4)-(9/4-9/5)+(11/5-11/6)-(13/6-13/7)+(15/7-15/8)-(17/8-17/9)
=7/3-(7/4+9/4)+(9/5+11/5)-(11/6+13/6)+(13/7+15/7)-(15/8+17/8)+17/9
=7/3-4+4-4+4-4+17/9
=1/3-1/9
=2/9