$$ \begin{aligned} \frac{8}{x} &= \frac{5}{x}-1&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{8}{x} &= x\cdot\frac{5}{x}-x\cdot1&& \text{cancel out the denominators} \\[1 em]8 &= 5-x&& \text{ swap the left and right side of the equation } \\[1 em]5-x &= 8&& \text{ move 5 to the right } \\[1 em]-x &= 8-5&& \\[1 em]-x &= 3&& \text{switch signs on both sides} \\[1 em]x &= -3&& \\[1 em] \end{aligned} $$

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