Bài 1:

a)  \(x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)

\(x-\frac{20}{2}.\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10.\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10\cdot\frac{4}{55}=\frac{3}{11}\)

\(x-\frac{8}{11}=\frac{3}{11}\)

\(x=1\)

b) \(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x.\left(x+1\right)}=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(2.\left(\frac{1}{6}-\frac{1}{x+1}\right)=\frac{2}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

=> x + 1 =18

x = 17

bài 2 ko bk lm, xl nha

mk cảm ơn bn nha

\(\frac{6}{11}x=\frac{9}{2}y=\frac{18}{5}z\Rightarrow\frac{6x}{11.18}=\frac{9y}{2.18}=\frac{18z}{5.18}\)

\(\Rightarrow\frac{-x}{-33}=\frac{y}{4}=\frac{z}{5}=\frac{-x+y+z}{-33+4+5}=\frac{-120}{-24}=5\)

\(\Rightarrow x=165;y=20;z=25\)

\(\begin{array}{l}a)x - \left( {\dfrac{5}{4} - \dfrac{7}{5}} \right) = \dfrac{9}{{20}}\\x = \dfrac{9}{{20}} + \left( {\dfrac{5}{4} - \dfrac{7}{5}} \right)\\x = \dfrac{9}{{20}} + \dfrac{{25}}{{20}} - \dfrac{{28}}{{20}}\\x = \dfrac{{6}}{{20}}\\x = \dfrac{{ 3}}{{10}}\end{array}\)

Vậy \(x = \dfrac{{ 3}}{{10}}\)

\(\begin{array}{*{20}{l}}{b)9 - x = \dfrac{8}{7} - \left( { - \dfrac{7}{8}} \right)}\\\begin{array}{l}9 - x = \dfrac{8}{7} + \dfrac{7}{8}\\9 - x = \dfrac{{64}}{{56}} + \dfrac{{49}}{{56}}\\9 - x = \dfrac{{113}}{{56}}\end{array}\\{x = 9 - \dfrac{{113}}{{56}}}\\{x = \dfrac{{504}}{{56}} - \dfrac{{113}}{{56}}}\\{x = \dfrac{{391}}{{56}}}\end{array}\)

Vậy \(x = \dfrac{{391}}{{56}}\)

a/ \(\frac{15}{x}-\frac{1}{3}=\frac{28}{51}\)

\(\frac{15}{x}=\frac{28}{51}+\frac{1}{3}\)

\(\frac{15}{x}=\frac{15}{17}\)

\(x=15:\frac{15}{17}\)

\(x=17\)

b) \(\frac{x}{20}-\frac{2}{5}=10\)

\(\frac{x}{20}=10+\frac{2}{5}\)

\(\frac{x}{20}=\frac{52}{5}\)

\(x=\frac{52}{5}\cdot20\)

\(x=208\)

c) \(x+\frac{18}{23}=2\frac{1}{3}\)

\(x+\frac{18}{23}=\frac{7}{3}\)

\(x=\frac{7}{3}-\frac{18}{23}\)

\(x=\frac{107}{69}\)

d) \(\frac{7}{11}< x-\frac{1}{7}< \frac{10}{13}\)

\(\Rightarrow\frac{7}{11}+\frac{1}{7}< x< \frac{10}{13}\)

\(\frac{60}{77}< x< \frac{60}{78}\)

Đến đây .....bí!

e) Tớ bỏ luôn đc ko.

D) 7/11<X-1/7<10/13

    <=> 7/11+1/7<x< 10/13+1/7

 <=> 60/77< x< 83/91

<=> 5460/1001 <x< 6391/1001

vậy X thuộc tập hợp các phÂN số lớn hơn 5460/1001 và bé hơn 913/1001

vd :  Y/1001 trong đó y là 5461;5462;5463...6389;6390

e) 7/9<13/11-x<15/16

<=> 7/9-13/11<-x< 15/16 -13/11

<=> -40/99< -x< -43/176

<=> 43/99< x < 40/176( nhân với -1 nên đổi dấu )

<=> 387/1584 < x< 640/1584

<=> vậy X là các phân số có dạng y/1584 , trong đó Y là 388;389;390 ........ 639

x+7 / -20 = -5/ x+7

(x+7)(x+7) = -20 .(-5)

(x+7)²= 100

=> ( x+7)²= 10²

=> x+7= 10

x= 10-7

x= 3

Vậy.....

\(\frac{x+7}{-20}=\frac{-5}{x+7}\left(x\ne7\right)\)

<=> (x+7)²=100

<=> \(\orbr{\begin{cases}x+7=10\\x+7=-10\end{cases}\Leftrightarrow\orbr{\begin{cases}x=3\\x=-17\end{cases}}}\)

suy ra (x+7)² = 100=10²

suy ra \(\orbr{\begin{cases}x+7=10\\x+7=-10\end{cases}\Rightarrow\orbr{\begin{cases}x=3\\x=-17\end{cases}}}\)

\(x=\frac{903}{391}\)

Bài này sử dụng MTCT đó bạn!

903/391 mình nghĩ vậy

x = 903/391

Bạn ghi sai đề chỗ 3/11 là sai mà phải 2/11 với là chỗ 2/7 là sai mà là 2/9

\(A=\frac{\frac{2}{5}-\frac{2}{7}+\frac{2}{11}}{\frac{7}{5}-\frac{7}{9}-\frac{7}{11}}:\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{6}-\frac{7}{8}+\frac{7}{10}}=\frac{2\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}{7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{11}\right)}:\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{7\left(\frac{1}{6}-\frac{1}{8}+\frac{1}{10}\right)}\)

\(=\frac{2}{7}:\frac{\frac{1}{3}-\frac{1}{4}+\frac{1}{5}}{\frac{7}{2}.\left(\frac{1}{3}-\frac{1}{8}+\frac{1}{10}\right)}=\frac{2}{7}:\frac{2}{7}=1\)

b,\(A.x+\frac{5}{6}=-\frac{3}{4}\)

<=>\(1.x=-\frac{3}{5}-\frac{5}{6}\)

<=>x=-43/30

Ai thấy mình làm đúng thì tích nha.Ai tích mình mình tích lại

a,A=1863/623:2/7

A=1863/178

b,

ta có:

1863/178.x+5/6=-3/4

1863/178.x=-19/12

=>x=-1691/11178