\(\frac{x-1}{13}+\frac{x-3}{11}+\frac{x+1}{15}=\frac{x+37}{17}\)
\(\Rightarrow x\left(\frac{1}{13}+\frac{1}{11}+\frac{1}{15}-\frac{1}{17}\right)=\frac{37}{17}+\frac{1}{13}+\frac{3}{11}-\frac{1}{15}\)
\(\Rightarrow x=\frac{\frac{37}{17}+\frac{1}{13}+\frac{3}{11}-\frac{1}{15}}{\frac{1}{13}+\frac{1}{11}+\frac{1}{15}-\frac{1}{17}}\)
=> x = 14
\(\Leftrightarrow\left(\frac{x-1}{13}-1\right)+\left(\frac{x-3}{11}-1\right)+\left(\frac{x+1}{15}-1\right)=\frac{x+37}{17}-3\)
\(\Leftrightarrow\frac{x-14}{13}+\frac{x-14}{11}+\frac{x-14}{15}=\frac{x-14}{17}\)
\(\Leftrightarrow\left(x-14\right)\left(\frac{1}{13}+\frac{1}{11}+\frac{1}{15}-\frac{1}{17}\right)=0\)
\(\Leftrightarrow x-14=0\) ( vì \(\frac{1}{13}+\frac{1}{11}+\frac{1}{15}-\frac{1}{17}\ne0\) )
\(\Leftrightarrow x=14\)
Vậy: Tập nghiệm của phương trình là: \(S=\left\{14\right\}\)