$$ \begin{aligned} 3 \cdot \frac{x}{x-2}-3 &= \frac{5}{x}&& \text{multiply ALL terms by } \color{blue}{ (x-2)x }. \\[1 em](x-2)x\cdot3 \cdot \frac{x}{x-2}-(x-2)x\cdot3 &= (x-2)x\cdot\frac{5}{x}&& \text{cancel out the denominators} \\[1 em]3x^2-(3x^2-6x) &= 5x-10&& \text{simplify left side} \\[1 em]3x^2-3x^2+6x &= 5x-10&& \\[1 em]3x^2-3x^2+6x &= 5x-10&& \\[1 em]6x &= 5x-10&& \text{move the $ \color{blue}{ 5x } $ to the left side} \\[1 em]6x-5x &= -10&& \text{simplify left side} \\[1 em]x &= -10&& \\[1 em]x &= -10&& \\[1 em] \end{aligned} $$

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