$$ \begin{aligned} \frac{1}{8}+5\frac{x}{x+2} &= \frac{5}{2}&& \text{multiply ALL terms by } \color{blue}{ 8(x+2)\cdot2 }. \\[1 em]8(x+2)\cdot2\cdot\frac{1}{8}+8(x+2)\cdot2\cdot5\frac{x}{x+2} &= 8(x+2)\cdot2\cdot\frac{5}{2}&& \text{cancel out the denominators} \\[1 em]2x+4+80x &= 40x+80&& \text{simplify left side} \\[1 em]82x+4 &= 40x+80&& \text{move the $ \color{blue}{ 40x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]82x-40x &= 80-4&& \text{simplify left and right hand side} \\[1 em]42x &= 76&& \text{ divide both sides by $ 42 $ } \\[1 em]x &= \frac{76}{42}&& \\[1 em]x &= \frac{38}{21}&& \\[1 em] \end{aligned} $$

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