\(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)-\left(\frac{x+8}{11}+1\right)-\left(\frac{x+10}{9}+1\right)-\left(\frac{x+12}{7}+1\right)=0\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{10}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7})\)
\(\Rightarrow x+19=0\)\(\left(Vì\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\ne0\right)\)
\(\Rightarrow x=-19\)
Ta có : \(\frac{x+2}{17}+\frac{x+4}{15}+\frac{x+6}{13}=\frac{x+8}{11}+\frac{x+10}{9}+\frac{x+12}{7}\)
\(\Rightarrow\left(\frac{x+2}{17}+1\right)+\left(\frac{x+4}{15}+1\right)+\left(\frac{x+6}{13}+1\right)=\left(\frac{x+8}{11}+1\right)+\left(\frac{x+10}{9}+1\right)+\left(\frac{x+12}{7}+1\right)\)
\(\Rightarrow\frac{x+19}{17}+\frac{x+19}{15}+\frac{x+19}{13}-\frac{x+19}{11}-\frac{x+19}{9}-\frac{x+19}{7}=0\)
\(\Rightarrow\left(x+19\right)\left(\frac{1}{17}+\frac{1}{15}+\frac{1}{13}-\frac{1}{11}-\frac{1}{9}-\frac{1}{7}\right)=0\)
\(\Rightarrow x+19=0\Rightarrow x=-19\)