$$\frac{3}{x}+2-\frac{5}{x} = \frac{13}{x}+2$$

$$ \begin{aligned} \frac{3}{x}+2-\frac{5}{x} &= \frac{13}{x}+2&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{3}{x}+x\cdot2-x\cdot\frac{5}{x} &= x\cdot\frac{13}{x}+x\cdot2&& \text{cancel out the denominators} \\[1 em]3+2x-5 &= 13+2x&& \text{simplify left and right hand side} \\[1 em]2x-2 &= 2x+13&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]2x-2x &= 13+2&& \text{simplify left and right hand side} \\[1 em]2x-2x &= 15&& \\[1 em]0 &= 15&& \\[1 em] \end{aligned} $$

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