$$\frac{x-1}{4}+\frac{x-1}{5} = \frac{1}{4}$$

$$ \begin{aligned} \frac{x-1}{4}+\frac{x-1}{5} &= \frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{x-1}{4}+20\frac{x-1}{5} &= 20\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]5x-5+4x-4 &= 5&& \text{simplify left side} \\[1 em]9x-9 &= 5&& \text{ move -9 to the right } \\[1 em]9x &= 5+9&& \\[1 em]9x &= 14&& \text{ divide both sides by $ 9 $ } \\[1 em]x &= \frac{14}{9}&& \\[1 em] \end{aligned} $$

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