$$ \begin{aligned} 2+\frac{1}{x^2} &= \frac{3}{x}&& \text{multiply ALL terms by } \color{blue}{ x^2x }. \\[1 em]x^2x\cdot2+x^2x\cdot\frac{1}{x^2} &= x^2x\cdot\frac{3}{x}&& \text{cancel out the denominators} \\[1 em]2x^3+\frac{1}{x^1} &= 3&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot2x^3+x^1\cdot\frac{1}{x^1} &= x^1\cdot3&& \text{cancel out the denominators} \\[1 em]2x^4+1 &= 3x&& \text{move all terms to the left hand side } \\[1 em]2x^4+1-3x &= 0&& \text{simplify left side} \\[1 em]2x^4-3x+1 &= 0&& \\[1 em] \end{aligned} $$

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