Ta có : 

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right).\frac{2}{9}=\frac{16}{9}\)

\(\Leftrightarrow\)\(x-2=\frac{16}{9}:\frac{2}{9}\)

\(\Leftrightarrow\)\(x-2=\frac{16}{9}.\frac{9}{2}\)

\(\Leftrightarrow\)\(x-2=\frac{8}{1}.\frac{1}{1}\)

\(\Leftrightarrow\)\(x-2=8\)

\(\Leftrightarrow\)\(x=8+2\)

\(\Leftrightarrow\)\(x=10\)

Vậy \(x=10\)

Chúc bạn học tốt ~ 

(x+x+x+x+x+x)-(2/12+2/20+2/30+2/42+2/56+2/72)=16/9
6x-4/9=16/9
6x=20/9=>x=20/7

Trả lời

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)

\(x-2\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{21}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(x-2\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)

\(x-2\cdot\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(x-2\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right)\cdot\frac{2}{9}=\frac{16}{9}\)

\(\)\(\Rightarrow2\left(x-2\right)=16\)

\(\Rightarrow x-2=16:2\)

\(\Rightarrow x-2=8\)

\(\Rightarrow x=8+2\)

\(\Rightarrow x=10\)

Vậy x=10

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)

\(\left(x-2\right)\cdot\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(\left(x-2\right)\cdot\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\cdot\left(\frac{3}{9}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\cdot\frac{2}{9}=\frac{16}{9}\)

\(x-2=\frac{16}{9}:\frac{2}{9}\)

\(x-2=\frac{16}{9}\cdot\frac{9}{2}\)

\(x-2=8\)

\(x=8+2\)

\(x=10\)

Vậy \(x=10\)

\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\)\(=\frac{16}{9}\)

\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right)\left(\frac{2}{9}\right)=\frac{16}{9}\)

2(x-2)=16

x-2=8

x=10
 

=> x-2.(1/12+1/20+1/30+1/42+1/56+1/72)=16/9

Đặt : Sáng = 1/12+1/20+1/30+1/42+1/56+1/72

=> Sáng = 1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=> Sáng = 1.(1/3-1/4+1/4-1/5+...+1/8-1/9

=> Sáng = 91.(1/3-1/9)

=> Sáng = 2/9

Thay Sáng vô biểu thức 1/12+1/20+1/30+1/42+1/56+1/72

Ta được :

x-2.2/9=16/9

giờ thì tự làm nha

=> x-2.(1/12+1/20+1/30+1/42+1/56+1/72)=16/9

Đặt : Sáng = 1/12+1/20+1/30+1/42+1/56+1/72

=> Sáng = 1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=> Sáng = 1.(1/3-1/4+1/4-1/5+...+1/8-1/9

=> Sáng = 91.(1/3-1/9)

=> Sáng = 2/9

Thay Sáng vô biểu thức 1/12+1/20+1/30+1/42+1/56+1/72

Ta được :

x-2.2/9=16/9

giờ thì tự làm nha

Ai k mk mk k lại

=> x-2.(1/12+1/20+1/30+1/42+1/56+1/72)=16/9

Đặt : Sáng = 1/12+1/20+1/30+1/42+1/56+1/72

=> Sáng = 1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=> Sáng = 1.(1/3-1/4+1/4-1/5+...+1/8-1/9

=> Sáng = 91.(1/3-1/9)

=> Sáng = 2/9

Thay Sáng vô biểu thức 1/12+1/20+1/30+1/42+1/56+1/72

Ta được :

x-2.2/9=16/9

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+..+\frac{x-2}{72}=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right).\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{72}\right)=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right).\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\right)=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right).\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Rightarrow x-2=0\Rightarrow x=2\)

sai rồi nha hoàng trung kiên

Ta có : 

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x-2}{42}+\frac{x-2}{56}+\frac{x-2}{72}=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right)\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\Leftrightarrow\)\(\left(x-2\right).\frac{2}{9}=\frac{16}{9}\)

\(\Leftrightarrow\)\(x-2=\frac{16}{9}:\frac{2}{9}\)

\(\Leftrightarrow\)\(x-2=\frac{16}{9}.\frac{9}{2}\)

\(\Leftrightarrow\)\(x-2=\frac{8}{1}.\frac{1}{1}\)

\(\Leftrightarrow\)\(x-2=8\)

\(\Leftrightarrow\)\(x=8+2\)

\(\Leftrightarrow\)\(x=10\)

Vậy \(x=10\)

Chúc bạn học tốt ~ 

\(\frac{x-2}{12}+\frac{x-2}{20}+\frac{x-2}{30}+\frac{x+2}{42} +\frac{x+2}{56}+\frac{x+2}{72}=\frac{16}{9}\)

\(\Rightarrow x-2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\right)=\frac{16}{9}\)

\(\Rightarrow x-2\left(\frac{1}{3}+\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-...+\frac{1}{8}-\frac{1}{8}+\frac{1}{9}\right)=\frac{16}{9}\)

\(\Rightarrow x-2\left(\frac{1}{3}+\frac{1}{9}\right)=\frac{16}{9}\)

\(\Rightarrow\left(x-2\right)\frac{4}{9}=\frac{16}{9}\)

\(\Rightarrow x-2=4\)

\(\Rightarrow x=6\)

Quên . Phải đóng ngoặc mấy chỗ x-2

\(\dfrac{x-2}{12}+\dfrac{x-2}{20}\dfrac{x-2}{30}+\dfrac{x-2}{42}+\dfrac{x-2}{56}+\dfrac{x-2}{72}=\dfrac{16}{9}\)

\(x-2.\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\right)=\dfrac{16}{9}\)

\(x-2.\left(\dfrac{1}{3}-\dfrac{1}{9}\right)=\dfrac{16}{9}\)

\(x-2=\dfrac{16}{9}:\dfrac{2}{9}\)

\(x-2=8\)

x=10

Vậy x bằng 10 thì thoả mãn đề bài

tich nhé đúng đấy

ớ ko có vế phải seo tính đc

à quên =10 chờ tí nhé

\(\frac{x-2}{3.4}+\frac{x-2}{4.5}+...+\frac{x-2}{8.9}=10\)

tới đây tự nghĩ là ra

x thuộc Z

\(\left(x-2\right):\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\right)=\frac{16}{9}\)

\(\left(x-2\right):\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\right)=\frac{16}{9}\)

\(\left(x-2\right):\frac{2}{9}=\frac{16}{9}\)

\(x-2=\frac{32}{91}\)

\(x=\frac{32}{91}+2\)

\(x=\frac{212}{91}\)