$$ \begin{aligned} \frac{7}{4} &= \frac{5}{y}-2&& \text{multiply ALL terms by } \color{blue}{ 4y }. \\[1 em]4y\cdot\frac{7}{4} &= 4y\cdot\frac{5}{y}-4y\cdot2&& \text{cancel out the denominators} \\[1 em]7y &= 20-8y&& \text{move the $ \color{blue}{ -8y } $ to the left side} \\[1 em]7y+8y &= 20&& \text{simplify left side} \\[1 em]15y &= 20&& \text{ divide both sides by $ 15 $ } \\[1 em]y &= \frac{20}{15}&& \\[1 em]y &= \frac{4}{3}&& \\[1 em] \end{aligned} $$

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