$$\frac{x}{x}+2 = \frac{10}{15}$$

$$ \begin{aligned} \frac{x}{x}+2 &= \frac{10}{15}&& \text{multiply ALL terms by } \color{blue}{ x\cdot15 }. \\[1 em]x\cdot15 \cdot \frac{x}{x}+x\cdot15\cdot2 &= x\cdot15\cdot\frac{10}{15}&& \text{cancel out the denominators} \\[1 em]15x+30x &= 10x&& \text{simplify left side} \\[1 em]45x &= 10x&& \text{move the $ \color{blue}{ 10x } $ to the left side} \\[1 em]45x-10x &= 0&& \text{simplify left side} \\[1 em]35x &= 0&& \text{ divide both sides by $ 35 $ } \\[1 em]x &= \frac{0}{35}&& \\[1 em]x &= 0&& \\[1 em] \end{aligned} $$

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