$$7+\frac{3}{x} = \frac{7}{x}+9$$

$$ \begin{aligned} 7+\frac{3}{x} &= \frac{7}{x}+9&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot7+x\cdot\frac{3}{x} &= x\cdot\frac{7}{x}+x\cdot9&& \text{cancel out the denominators} \\[1 em]7x+3 &= 7+9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]7x-9x &= 7-3&& \text{simplify left and right hand side} \\[1 em]-2x &= 4&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= -\frac{4}{2}&& \\[1 em]x &= -2&& \\[1 em] \end{aligned} $$

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