$$ \begin{aligned} 6399\cdot\frac{13}{8}+\frac{353}{x} &= 10444&& \text{multiply ALL terms by } \color{blue}{ 8x }. \\[1 em]8x\cdot6399\cdot\frac{13}{8}+8x\cdot\frac{353}{x} &= 8x\cdot10444&& \text{cancel out the denominators} \\[1 em]83187x+2824 &= 83552x&& \text{move the $ \color{blue}{ 83552x } $ to the left side and $ \color{blue}{ 2824 }$ to the right} \\[1 em]83187x-83552x &= -2824&& \text{simplify left side} \\[1 em]-365x &= -2824&& \text{ divide both sides by $ -365 $ } \\[1 em]x &= \frac{-2824}{-365}&& \\[1 em]x &= \frac{2824}{365}&& \\[1 em] \end{aligned} $$

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