$$ \begin{aligned} \frac{10}{4} &= n+\frac{8}{8}&& \text{multiply ALL terms by } \color{blue}{ 8 }. \\[1 em]8\cdot\frac{10}{4} &= 8n+8\cdot\frac{8}{8}&& \text{cancel out the denominators} \\[1 em]20 &= 8n+8&& \text{ swap the left and right side of the equation } \\[1 em]8n+8 &= 20&& \text{ move 8 to the right } \\[1 em]8n &= 20-8&& \\[1 em]8n &= 12&& \text{ divide both sides by $ 8 $ } \\[1 em]n &= \frac{12}{8}&& \\[1 em]n &= \frac{3}{2}&& \\[1 em] \end{aligned} $$

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