$$ \begin{aligned} \frac{15}{b} &= \frac{23}{b}+14&& \text{multiply ALL terms by } \color{blue}{ b }. \\[1 em]b\cdot\frac{15}{b} &= b\cdot\frac{23}{b}+b\cdot14&& \text{cancel out the denominators} \\[1 em]15 &= 23+14b&& \text{ swap the left and right side of the equation } \\[1 em]23+14b &= 15&& \text{ move 23 to the right } \\[1 em]14b &= 15-23&& \\[1 em]14b &= -8&& \text{ divide both sides by $ 14 $ } \\[1 em]b &= -\frac{8}{14}&& \\[1 em]b &= -\frac{4}{7}&& \\[1 em] \end{aligned} $$

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