$$ \begin{aligned} 2+\frac{7}{b} &= \frac{2}{5}&& \text{multiply ALL terms by } \color{blue}{ b\cdot5 }. \\[1 em]b\cdot5\cdot2+b\cdot5\cdot\frac{7}{b} &= b\cdot5\cdot\frac{2}{5}&& \text{cancel out the denominators} \\[1 em]10b+35 &= 2b&& \text{move the $ \color{blue}{ 2b } $ to the left side and $ \color{blue}{ 35 }$ to the right} \\[1 em]10b-2b &= -35&& \text{simplify left side} \\[1 em]8b &= -35&& \text{ divide both sides by $ 8 $ } \\[1 em]b &= -\frac{35}{8}&& \\[1 em] \end{aligned} $$

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