$$\frac{x-5}{2}+\frac{x+3}{3} = 6$$

$$ \begin{aligned} \frac{x-5}{2}+\frac{x+3}{3} &= 6&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x-5}{2}+6\frac{x+3}{3} &= 6\cdot6&& \text{cancel out the denominators} \\[1 em]3x-15+2x+6 &= 36&& \text{simplify left side} \\[1 em]5x-9 &= 36&& \text{ move -9 to the right } \\[1 em]5x &= 36+9&& \\[1 em]5x &= 45&& \text{ divide both sides by $ 5 $ } \\[1 em]x &= \frac{45}{5}&& \\[1 em]x &= 9&& \\[1 em] \end{aligned} $$

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