题目

8/15-12/35+16/63-20/99+24/143-28/195

提问时间：2020-08-07

答案

8/15-12/35+16/63-20/99+24/143-28/195
=[(8*7)/(3*5*7)-(12*3)/(3*5*7)]+[(16*11)/(7*9*11)-(20*7)/(7*9*11)]+[(24*15)/(11*13*15)-(28*11)/ (11*13*15)]
=(8*7-12*3)/(3*5*7)+(16*11-20*7)/(7*9*11)+(24*15-28*11)/(11*13*15
=20/(3*5*7)+36/(7*9*11)+52/(11*13*15)
=4/(3*7)+4/(7*11)+4/(11*15)
=(4*11+4*3)/(3*7*11)+4/(11*15)
=56/(3*7*11)+4/(11*15)
=8/(3*11)+4/(11*15)
=(8*15+4*3)/(3*11*15)
=132/(3*11*15)
=12/(3*15)
=4/15