ta có \(x+1.x+1=8.2=16\)

           \(x+1.x+1=4^2\)

            \(x+1=4\)

             \(x=3\)

Theo đầu bài ta có:
\(\frac{x+1}{2}=\frac{8}{x+1}\)
\(\Rightarrow\left(x+1\right)\left(x+1\right)=2\cdot8\)
\(\Rightarrow\left(x+1\right)^2=16\)
\(\Rightarrow x+1=\sqrt{16}\)
\(\Rightarrow x=4-1\)
\(\Rightarrow x=3\)

\(\frac{x+1}{2}\)=\(\frac{8}{x+1}\)Từ đây suy ra : x = 8:2=4 ; Thử đúng

\(\frac{3}{2}x-\frac{11}{5}=\frac{7}{8}.\frac{64}{49}\)

\(\frac{3}{2}x-\frac{11}{5}=\frac{8}{7}\)

\(\frac{3}{2}x=\frac{8}{7}+\frac{11}{5}=\frac{117}{35}\)

\(x=\frac{117}{35}:\frac{3}{2}=\frac{78}{35}\)

\(\frac{3}{2}x-\frac{11}{5}=\frac{7}{8}.\frac{64}{49}\) 

\(\frac{3}{2}x-\frac{11}{5}=\frac{8}{7}\)

\(\frac{3}{2}x=\frac{8}{7}+\frac{11}{5}\)

\(\frac{3}{2}x=\frac{117}{35}\)

\(x=\frac{117}{35}:\frac{3}{2}\)

\(x=\frac{78}{35}\)

\(\frac{-2}{3}.x+\frac{1}{5}=\frac{3}{10}\)

  \(\frac{-2}{3}.x=\frac{3}{10}-\frac{1}{5}=\frac{1}{10}\)

           \(x=\frac{1}{10}:\frac{-2}{3}=-\frac{3}{20}\)

x=4 cách lm tính vế trái sau đó đc -16/625 suy ra x= 4

\(\left(2\frac{1}{3}+3\frac{1}{2}\right):\left(x+3\frac{1}{7}\right)+7\frac{1}{2}=1\frac{69}{86}\)

\(\left(\frac{7}{3}+\frac{7}{2}\right):\left(x+\frac{22}{7}\right)+\frac{15}{2}=\frac{155}{86}\)

\(\left(\frac{14}{6}+\frac{21}{6}\right):\left(x+\frac{22}{7}\right)+\frac{15}{2}=\frac{155}{86}\)

 \(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{155}{86}-\frac{15}{2}\)

\(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{155}{86}-\frac{645}{86}\)

 \(\frac{35}{6}:\left(x+\frac{22}{7}\right)=\frac{-245}{43}\)

 \(x+\frac{22}{7}=\frac{35}{6}:\frac{-245}{43}=\frac{35}{6}\cdot\frac{-43}{245}\)

\(x+\frac{22}{7}=\frac{-43}{42}\)

\(x=\frac{-43}{42}-\frac{22}{7}=\frac{-43}{42}-\frac{132}{42}\)

 \(x=\frac{-25}{6}\)