$$\frac{7}{x}+\frac{1}{4} = \frac{9}{x}$$

$$ \begin{aligned} \frac{7}{x}+\frac{1}{4} &= \frac{9}{x}&& \text{multiply ALL terms by } \color{blue}{ x\cdot4 }. \\[1 em]x\cdot4\cdot\frac{7}{x}+x\cdot4\cdot\frac{1}{4} &= x\cdot4\cdot\frac{9}{x}&& \text{cancel out the denominators} \\[1 em]28+x &= 36&& \text{ move 28 to the right } \\[1 em]x &= 36-28&& \\[1 em]x &= 8&& \\[1 em]x &= 8&& \\[1 em] \end{aligned} $$

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