$$ \begin{aligned} 5 \cdot \frac{x+3}{6} &= 3 \cdot \frac{x-1}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30\cdot5 \cdot \frac{x+3}{6} &= 30\cdot3 \cdot \frac{x-1}{5}&& \text{cancel out the denominators} \\[1 em]25x+75 &= 18x-18&& \text{move the $ \color{blue}{ 18x } $ to the left side and $ \color{blue}{ 75 }$ to the right} \\[1 em]25x-18x &= -18-75&& \text{simplify left and right hand side} \\[1 em]7x &= -93&& \text{ divide both sides by $ 7 $ } \\[1 em]x &= -\frac{93}{7}&& \\[1 em] \end{aligned} $$

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