$$ \begin{aligned} \frac{3x-1}{2}+\frac{4x+1}{3} &= \frac{40+6x}{5}&& \text{multiply ALL terms by } \color{blue}{ 30 }. \\[1 em]30 \cdot \frac{3x-1}{2}+30\frac{4x+1}{3} &= 30 \cdot \frac{40+6x}{5}&& \text{cancel out the denominators} \\[1 em]45x-15+40x+10 &= 36x+240&& \text{simplify left side} \\[1 em]85x-5 &= 36x+240&& \text{move the $ \color{blue}{ 36x } $ to the left side and $ \color{blue}{ -5 }$ to the right} \\[1 em]85x-36x &= 240+5&& \text{simplify left and right hand side} \\[1 em]49x &= 245&& \text{ divide both sides by $ 49 $ } \\[1 em]x &= \frac{245}{49}&& \\[1 em]x &= 5&& \\[1 em] \end{aligned} $$

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