能简算的要简算 1/30＋1/42＋1/56＋1/72

题目

能简算的要简算 1/30＋1/42＋1/56＋1/72
能简算的要简算
1/30＋1/42＋1/56＋1/72

答案

1/(5×6)+1/(6×7)+1/(7×8)+1/(8×9)
=(1×7)/(5×6×7)+(1×5)/(5×6×7)+(1×9)/(7×8×9)+(1×7)/(7×8×9)
=7/(5×6×7)+5/(5×6×7)+9/(7×8×9)+7/(7×8×9)
=(5+7)/(5×6×7)+(7+9)/(7×8×9)
=12/(5×6×7)+16/(7×8×9)
=(2×6)/(5×6×7)+(2×8)/(7×8×9)
=2/(5×7)+2/(7×9)
=(2×9)/(5×7×9)+(2×5)/(5×7×9)
=(2×14)/(5×7×9)
=(2×2×7)/(5×7×9)
=(2×2)/(5×9)
=4/45