\(A=\frac{5}{3\cdot7}+\frac{5}{7\cdot11}+\frac{5}{11\cdot15}+...+\frac{5}{35\cdot39}\)

\(=\frac{5}{4}\cdot\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{35\cdot39}\right)\)

\(=\frac{5}{4}\cdot\left(1-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...-\frac{1}{35}+\frac{1}{35}-\frac{1}{39}\right)\)

\(=\frac{5}{4}\cdot\left(1-\frac{1}{39}\right)=\frac{5}{4}\cdot\frac{38}{39}=\frac{95}{78}\)

Đề là tính hay tính nhanh vậy cậu?
 

cong tru da thuc la nhu the nao

??????

 `A) 1/3 + 1/5 - 1/4 = 20/60 + 12/60 - 15/60 = 17/60`

` B) 7/8 - ( 1/4 + 2/5 ) = 7/8 - 2/4 -2/5 = 5/8-2/8 = 9/40`

` C) 5/11 - ( 3/5 - 6/11 ) = 5/11 - 3/55 = 25/55 - 3/55 = 22/55=2/5 ` 

` D) 5/7 - ( 19/35 - 6/15 ) = 5/7 - 1/7 = 4/7 `

`1/3 + 1/5 -1/4`

`= 5/15 + 3/15 -1/4`

`= 8/15 -1/4`

`=  17/60`

__

`7/8 -(1/4 + 2/5)`

`= 7/8-1/4 - 2/5`

`= 7/8 - 2/8 -2/5`

`= 5/8 -2/5`

`= 9/40`

__

`5/11-(3/5 -6/11)`

`= 5/11 -3/5 +6/11`

`= (5/11 + 6/11)-3/5`

`= 1 -3/5`

`= 5/5-3/5`

`=2/5`

__

`5/7 - ( 19/35 - 6/15)`

`= 5/7 - 19/35 + 6/15`

`= 25/35 -19/35 + 6/15`

`=6/35 +6/15`

`=4/7`

(4+11):15+(35+64):99+(2+5):7=15:15+99:99+7:7=1+1+1=3

`4/15+35/99+11/15-2/7+64/99-5/7`

`=(4/15+11/15)+(35/99+64/99)-(2/7+5/7)`

`=15/15+99/99-7/7`

`=1+1-1`

`=2-1`

`=1`

1

bằng 13/15 bạn ạ 

a: =35/17-18/17-9/5+4/5

=1-1=0

b: =-7/19(3/17+8/11-1)

=7/19*18/187=126/3553

c: =26/15-11/15-17/3-6/13

=1-6/13-17/3

=7/13-17/3=-200/39