$$ \begin{aligned} 2+\frac{5}{x}+\frac{3}{x^2} &= 0&& \text{multiply ALL terms by } \color{blue}{ xx^2 }. \\[1 em]xx^2\cdot2+xx^2\cdot\frac{5}{x}+xx^2\cdot\frac{3}{x^2} &= xx^2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^3+5+\frac{3}{x^1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot2x^3+x^1\cdot5+x^1\cdot\frac{3}{x^1} &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]2x^4+5x+3 &= 0&& \\[1 em] \end{aligned} $$

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