32/3 x 7 + 6/7 x 41 + 9/41 x 10 + 1/51 x 10 + 19/51 x 14

Đáp án:

`A=67/42`

Lời giải:

`{32}/{3 . 7} + {6}/{7 . 41} + {9}/{41 . 10} + {1}/{51 . 10} + {19}/{51 . 14}`

Nhân cả hai vế với `1/5` ta được:

`=>1/5A=1/5.(\frac{32}{3.7}+\frac{6}{7.41}+\frac{9}{41.10}+\frac{1}{51.10}+\frac{19}{51.14})`

`=>1/5A=\frac{32}{3.5.7}+\frac{6}{5.7.41}+\frac{9}{5.10.41}+\frac{1}{5.10.51}+\frac{19}{5.14.51}`

`=>1/5A=\frac{32}{35.3}+\frac{6}{35.41}+\frac{9}{50.41}+\frac{1}{50.51}+\frac{19}{51.70}`

`=>1/5A=\frac{35-3}{35.3}+\frac{41-35}{35.41}+\frac{50-41}{50.41}+\frac{50-51}{50.51}+\frac{70-51}{51.70}`

`=>1/5A=1/3-1/35+1/35-1/41+1/41-1/50+1/50-1/51+1/51-1/70`

`=>1/5A=1/3+(1/35-1/35)+(1/41-1/41)+(1/50-1/50)-1/70`

`=>1/5A=1/3-1/70+0`

`=>1/5A=1/3-1/70`

`=>1/5A=70/210-3/210`

`=>1/5A=67/210`

`=>A=67/210: 1/5`

`=>A=67/210.5`

`=>A=\frac{67.5}{210}`

`=>A=\frac{67.5}{42.5}`

`=>A=67/42`

Vậy `A=67/42`