Solve $\dfrac{6x + 1}{15} - \dfrac{2x - 4}{7x - 1} = \dfrac{2x - 1}{5}$:

Grouping the two terms with denominators $15$ and $5$ on one side reduces them to the constant $\frac{4}{15}$, so the equation becomes $\frac{4}{15}=\frac{2x-4}{7x-1}$. Cross-multiplying gives $4(7x-1)=15(2x-4)$, i.e. $28x-4=30x-60$, hence $x=28$.