\(\overline{A9876A}⋮2\) => A chẵn

\(\overline{A9876A}⋮9\Rightarrow2A+9+8+7+6=2A+30=2A+3+27⋮9\)

\(27⋮9\Rightarrow2A+3⋮9\) 

A chẵn => 2A+3 lẻ

\(A\le9\Rightarrow2A+3\le21\)

\(\Rightarrow2A+3=9\Rightarrow A=3\)

A9876A nha. Mình viết nhầm

Tử số:

\(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{98}+\dfrac{1}{100}\)

\(=(\dfrac{1}{2}+\dfrac{1}{100})+(\dfrac{1}{4}+\dfrac{1}{98})+...+\left(\dfrac{1}{48}+\dfrac{1}{54}\right)+(\dfrac{1}{50}+\dfrac{1}{52})\)

\(=\dfrac{102}{2.100}+\dfrac{102}{4.98}+...+\dfrac{102}{48.54}+\dfrac{102}{50.52}\)

\(=102\left(\dfrac{1}{2.100}+\dfrac{1}{4.98}+...+\dfrac{1}{48.54}+\dfrac{1}{50.52}\right)\)

Mẫu số:

\(\dfrac{1}{2.100}+\dfrac{1}{4.98}+...+\dfrac{1}{98.4}+\dfrac{1}{100.2}\)

\(=\dfrac{2}{2.100}+\dfrac{2}{4.98}+....+\dfrac{2}{48.54}+\dfrac{2}{50.52}\)

\(=2\left(\dfrac{1}{2.100}+\dfrac{1}{4.98}+...+\dfrac{1}{48.54}+\dfrac{1}{50.52}\right)\)

Chia cả tử và mẫu cho \(=\dfrac{1}{2.100}+\dfrac{1}{4.98}+...+\dfrac{1}{48.54}+\dfrac{1}{50.52}\)

ta được \(\dfrac{tử}{mẫu}=\dfrac{102}{2}=51\)

Đs:....

b, \(\dfrac{x}{3}\) - \(\dfrac{1}{2}\) = \(\dfrac{1}{5}\) 

    \(\dfrac{x}{3}\)       = \(\dfrac{1}{5}\) + \(\dfrac{1}{2}\) 

     \(\dfrac{x}{3}\)      = \(\dfrac{7}{10}\)

       x = \(\dfrac{7}{10}\) x 3 

        x = 21/10

c,    x + \(\dfrac{1}{2}\) = \(\dfrac{6}{10}\)

              x = \(\dfrac{6}{10}\) - \(\dfrac{1}{2}\)

              x = \(\dfrac{1}{10}\)

d,    x   +  \(\dfrac{3}{15}\) =  \(\dfrac{1}{3}\)

                  x = \(\dfrac{1}{3}\) - \(\dfrac{3}{15}\)

                 x = \(\dfrac{2}{15}\)

h,  \(\dfrac{4}{5}\)   + x = \(\dfrac{2}{3}\)  

              x = \(\dfrac{2}{3}\) - \(\dfrac{4}{5}\)

             x = \(\dfrac{-2}{15}\)

b, x=21/10

c,x=1/10

d,x= 2/15

h,x=-2/15

\(\dfrac{1}{3}.\dfrac{4}{5}+\dfrac{1}{3}.\dfrac{6}{5}-\dfrac{4}{3}\)

\(=\dfrac{1}{3}.\left(\dfrac{4}{5}+\dfrac{6}{5}\right)-\dfrac{4}{3}\)

\(=\dfrac{1}{3}.2-\dfrac{4}{3}\)

\(=\dfrac{2}{3}-\dfrac{4}{3}=-\dfrac{2}{3}\)

1/3 . 4/5 + 1/3 . 6/5 - 4/3 

= 1/3 . ( 4/5 + 6/5 )  - 4/3

= 1/3 . 10 - 4/3

=10/3 - 4/3

=6/3

a) \(A=\dfrac{x+5}{x+1}=1+\dfrac{4}{x+1}\)

Để \(A\in Z\Rightarrow\left(x+1\right)\inƯ\left(4\right)=\left\{\pm1;\pm2;\pm4\right\}\)

\(\Rightarrow x\in\left\{0;-2;1;-3;3;-5\right\}\)

b) \(B=\dfrac{2x+4}{x+3}=\dfrac{2\left(x+3\right)-2}{x+3}=2-\dfrac{2}{x+3}\)

Để \(B\in Z\Rightarrow\left(x+3\right)\inƯ\left(2\right)=\left\{\pm1;\pm2\right\}\)

\(\Rightarrow x\in\left\{-2;-4;-1;-5\right\}\)

c) \(C=\dfrac{3x+8}{x-1}=\dfrac{3\left(x-1\right)+11}{x-1}=3+\dfrac{11}{x-1}\)

Để \(C\in Z\Rightarrow\left(x-1\right)\inƯ\left(11\right)=\left\{\pm1;\pm11\right\}\)

\(\Rightarrow x\in\left\{2;0;12;-10\right\}\)

\(\dfrac{1}{2014}-\dfrac{1}{2014.2013}-...-\dfrac{1}{3.2}-\dfrac{1}{2.1}\\ =\dfrac{1}{2014}-\left(\dfrac{1}{2013}-\dfrac{1}{2014}\right)-...-\left(\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(1-\dfrac{1}{2}\right)\\ =\dfrac{1}{2014}+\dfrac{1}{2014}-\dfrac{1}{2013}+\dfrac{1}{2013}-\dfrac{1}{2012}+...+\dfrac{1}{3}-\dfrac{1}{2}+\dfrac{1}{2}-1\\ =\dfrac{1}{2014}+\dfrac{1}{2014}-1\\ =\dfrac{1}{1007}-1\\ =-\dfrac{1006}{1007}\)

Lấy hiệu hai phân số rồi suy ra điều phải chứng minh

\(\dfrac{-214}{317}-\dfrac{-21}{38}=\dfrac{21.317-214.38}{317.38}=\dfrac{-1475}{317.38}< 0\)

\(\Rightarrow\dfrac{-214}{317}< \dfrac{-21}{38}\)

giúp mình đi mà

Làm nhanh giúp mình với

\(\dfrac{23}{45}>\dfrac{23}{46}=\dfrac{1}{2}\)

\(\dfrac{75}{151}< \dfrac{75}{150}=\dfrac{1}{2}\)

\(\Rightarrow\dfrac{23}{45}>\dfrac{75}{151}\)

Gọi a là chiều rộng đáy của hình hộp chữ nhật.

Ta có:

\(2.60.a=2.12.a+2.12.60\Leftrightarrow120a=24a+1440\)

\(\Leftrightarrow96a=1440\Rightarrow a=15\)

Vậy chiều rộng đáy của hình hộp chữ nhật là 15 cm