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

rút gọn thành

1/2 x 2/3 x 3/4 x 4/5 x 5/6 x 6/7 x 7/8 x 8/9

1x2x3x4x5x6x7x8

__________________

2x3x4x5x6x7x8x9

gạch các số giống nhau ở tử và mẫu và bằng 1/9

x-2/12 + x-2/20+....+x-2/72
=x-2/3.4+ x-2/ 4.5+...+x-2/8.9
=(x-2).1/3.4.1+(x-2).1/4.5.1+......+(x-2).1/8.9.1
=x-2/1(1/3.4+1/4.5+....+1/8.9)
=x-2(1/3 -1/4 +1/4 -1/5+...+1/8-1/9)
=x-2(1/3-1/9)
=(x-2).2/9
=2x-4/9

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

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

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

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

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

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

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

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

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

\(x-2=8\)

\(x=8+2\)

\(x=10\)

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
 

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

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

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

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

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

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

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 ~