$$ \begin{aligned} 6 \cdot \frac{x-1}{12} &= 4 \cdot \frac{x+1}{12}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12\cdot6 \cdot \frac{x-1}{12} &= 12\cdot4 \cdot \frac{x+1}{12}&& \text{cancel out the denominators} \\[1 em]6x-6 &= 4x+4&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]6x-4x &= 4+6&& \text{simplify left and right hand side} \\[1 em]2x &= 10&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{10}{2}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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