Ta có: \(\left(\dfrac{1}{57}-\dfrac{1}{5757}+\dfrac{1}{23}\right)\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)

\(=\left(\dfrac{1}{57}-\dfrac{1}{5757}+\dfrac{1}{23}\right)\cdot\left(\dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6}\right)\)

=0

\(\left(\dfrac{1}{57}-\dfrac{1}{5757}+\dfrac{1}{23}\right).\left(\dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6}\right)\)= 0

E = \(\left(\frac{1}{57}-\frac{1}{5757}+\frac{1}{23}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)

E = \(\left(\frac{1}{57}-\frac{1}{5757}+\frac{1}{23}\right).0\)

E = 0

(1/57 + 1/5757 + 1/23 ) . ( 1/2 - 1/3 - 1/6 )

= ( 1/57 + 1/5757 + 1/23 ) . ( 3/6 - 2/6 - 1/6 )

= (1/57 + 1/5757 + 1/23 )  .  0

= 0

\(\left(\frac{1}{57}+\frac{1}{5757}+\frac{1}{23}\right).\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)

\(=\left(\frac{1}{57}+\frac{1}{5757}+\frac{1}{23}\right).0\)

\(=0\)

chúc bạn học tốt

bài này mình làm được nhưng mà dài vậy sao làm nổi 

Các bạn ơi cố gắng giúp mk đi mk sắp thi rồi

nhưng bạn ơi mk không biết đánh dấu giá tri ''dấu ích'' chỉ giúp mk rồi mk làm cho

a) \(\frac{53}{101}\cdot-\frac{13}{97}+\frac{53}{101}\cdot-\frac{84}{97}\)

\(=\frac{53}{101}\cdot\left(-\frac{13}{97}-\frac{84}{97}\right)\)

\(=\frac{53}{101}\cdot\left(-1\right)\)

\(=-\frac{53}{101}\)

1) a) \(\frac{5454}{5757}-\frac{171717}{191919}=\frac{18\times3\times101}{19\times3\times101}-\frac{17\times10101}{19\times10101}=\frac{18}{19}-\frac{17}{19}=\frac{1}{19}\)

b) \(\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times....\times\frac{2021}{2020}=\frac{6\times7\times8\times...\times2021}{5\times6\times7\times...\times2020}=\frac{2021}{5}\)

2) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}=2\times\frac{1}{6}+2\times\frac{1}{12}+2\times\frac{1}{20}+...+2\times\frac{1}{90}\)

\(=2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\)

\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=2\times\left(\frac{1}{2}-\frac{1}{10}\right)=2\times\frac{2}{5}=\frac{4}{5}\)

b)Vì \(a-1< a+1\)

=> \(\frac{1}{a-1}>\frac{1}{a+1}\)

1/ a x b = 1/a - 1/b 

đk : b - a = 1

1) (-1)³ + (-2)³ + (-3)³ - |x+5| = (5 - 6 -7)³

     (-1) -8 - 27 - |x+5| = -512

                         |x+5| = 476

=> x + 5 = 476 hoặc x + 5 = -476

     =>  x = 472           => x = -481

Vậy....

2) [(x-3)² - 9] . [(x-1)²-1]=0

    ( x - 3 - 3).(x - 3 + 3).(x - 1 - 1).(x - 1 +1) =0

    ( x - 6) . (x - 0) . (x - 2) . (x - 0) = 0

=> x - 6 = 0           hoặc        x - 0 = 0           hoặc x - 2 = 0

     => x = 6                            => x = 0                   => x = 2

Vậy...

3) 2.(x-23) - (x-43) = 96 - 115

     2x - 46 - x + 43 = -19

                           x = -16