$$\frac{1}{2x+5} = \frac{3}{x+5}$$

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

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