$$ \begin{aligned} \frac{2x+3}{4}+\frac{x-1}{2} &= \frac{3x+5}{6}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{2x+3}{4}+12\frac{x-1}{2} &= 12 \cdot \frac{3x+5}{6}&& \text{cancel out the denominators} \\[1 em]6x+9+6x-6 &= 6x+10&& \text{simplify left side} \\[1 em]12x+3 &= 6x+10&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]12x-6x &= 10-3&& \text{simplify left and right hand side} \\[1 em]6x &= 7&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{7}{6}&& \\[1 em] \end{aligned} $$

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