$$ \begin{aligned} 5 &= \frac{8-x}{x}&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot5 &= x \cdot \frac{8-x}{x}&& \text{cancel out the denominators} \\[1 em]5x &= 8-x&& \text{move the $ \color{blue}{ -x } $ to the left side} \\[1 em]5x+x &= 8&& \text{simplify left side} \\[1 em]6x &= 8&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{8}{6}&& \\[1 em]x &= \frac{4}{3}&& \\[1 em] \end{aligned} $$

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