$$ \begin{aligned} 1-\frac{4}{x} &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ x\cdot6 }. \\[1 em]x\cdot6\cdot1-x\cdot6\cdot\frac{4}{x} &= x\cdot6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]6x-24 &= 5x&& \text{move the $ \color{blue}{ 5x } $ to the left side and $ \color{blue}{ -24 }$ to the right} \\[1 em]6x-5x &= 24&& \text{simplify left side} \\[1 em]x &= 24&& \\[1 em]x &= 24&& \\[1 em] \end{aligned} $$

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