$$ \begin{aligned} 9+\frac{7}{x} &= 16&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot9+x\cdot\frac{7}{x} &= x\cdot16&& \text{cancel out the denominators} \\[1 em]9x+7 &= 16x&& \text{move the $ \color{blue}{ 16x } $ to the left side and $ \color{blue}{ 7 }$ to the right} \\[1 em]9x-16x &= -7&& \text{simplify left side} \\[1 em]-7x &= -7&& \text{ divide both sides by $ -7 $ } \\[1 em]x &= \frac{-7}{-7}&& \\[1 em]x &= 1&& \\[1 em] \end{aligned} $$

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