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a) Ta có: \(\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+...+\dfrac{3}{59\cdot61}\)

\(=\dfrac{3}{2}\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+...+\dfrac{2}{59\cdot61}\right)\)

\(=\dfrac{3}{2}\left(\dfrac{1}{5}-\dfrac{1}{61}\right)\)

\(=\dfrac{3}{2}\cdot\dfrac{56}{305}=\dfrac{84}{305}\)

14 tháng 7 2021

a)

3/5.7+3/7.9+...+3/59.61

=3/2.(2/5.7+2/7.9+...+2/59.61)

=3/2.(1/5−1/7+1/7−1/9+...+1/59−1/61)

=3/2(1/5−1/61)

=3/2.56/305

=844/305

b) câu b, bạn vt hơi khó hiểu

23 tháng 3 2016

mn giúp

14 tháng 4 2017

Này bạn làm sao để ra dấu phân số vậy

25 tháng 2 2022

\(A=\dfrac{5}{11}.\dfrac{5}{7}+\dfrac{5}{11}.\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}.1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=\dfrac{11}{11}=1\)

\(B=\dfrac{3}{13}.\dfrac{6}{11}+\dfrac{3}{13}.\dfrac{9}{11}-\dfrac{3}{13}.\dfrac{4}{11}=\dfrac{3}{13}\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}.1=\dfrac{3}{13}\)

\(C=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right)\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)=\left(\dfrac{12}{16}-\dfrac{31}{22}+\dfrac{14}{91}\right).0=0\)

17 tháng 4 2017

b,=1/5-1/7+1/7-1/9+...+1/59-1/61

=1/5-1/61

=54/115

28 tháng 3 2017

\(\frac{5}{4}\) \(+\) \(\frac{3}{13}\) \(-\) \(\frac{1}{2}\)

\(=\) \(\frac{77}{52}\) \(-\) \(\frac{1}{2}\)

\(=\) \(\frac{51}{52}\)

\(\frac{4}{13}\) \(-\) \(\frac{2}{11}\) \(+\) \(\frac{3}{2}\)

\(=\) \(\frac{18}{143}\) \(+\) \(\frac{3}{2}\)

\(=\) \(\frac{465}{286}\)

11 tháng 3 2021

a) \(\dfrac{\dfrac{3}{14}-\dfrac{3}{17}+\dfrac{3}{19}}{\dfrac{5}{19}+\dfrac{5}{14}-\dfrac{5}{17}}=\dfrac{3\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}{5\left(\dfrac{1}{14}-\dfrac{1}{17}+\dfrac{1}{19}\right)}=\dfrac{3}{5}\)

 

11 tháng 3 2021

c) \(\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{193}}{\dfrac{3}{7}+\dfrac{3}{5}+\dfrac{3}{17}-\dfrac{3}{293}}=\dfrac{2\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}{3\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{193}\right)}=\dfrac{2}{3}\)

d) 

28 tháng 2 2023

`a)3/5+(-4/9)`

`=3/5-4/9`

`=27/45-20/45`

`=7/45`

`b)3/5+2/5 . 15/8`

`=3/5 + 30/40`

`=3/5+3/4`

`=12/20+15/20`

`=27/20`

`c)7/2 . 8/13 + 8/13 . (-5/2)`

`=8/13 . (7/2 +(-5)/2)`

`=8/13 . 1`

`=8/13`

`d)-5/17 . (-9/23)+9/23 . (-22/17) + 11 9/23`

`=-5/17 . (-9/23) + 9/23 . (-1) . 22/17 + 11 + 9/23`

`=-5/17 . (-9/23) + (-9/23) . 22/17+11+9/23`

`= -9/23 ( -5/17 + 22/17)+11+9/23`

`= - 9/23 . 1+11+9/23`

`=-9/23+11+9/23`

`=(-9/23+9/23)+11`

`=0+11`

`=11`

a: =27/45-20/45=7/45

b: =3/5+30/40

=3/5+3/4

=12/20+15/20

=27/20

c: =8/13(7/2-5/2+1)=8/13*2=16/13

d: =9/23*5/17-9/23*22/17+11+9/23

=-9/23+11+9/23

=11