$$\frac{x+1}{x^2}-3x+2 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.18521 & x_2 = -0.25927+0.46263i & x_3 = -0.25927-0.46263i \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x+1}{x^2}-3x+2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\frac{x+1}{x^2}-x^2\cdot3x+x^2\cdot2 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]x+1-3x^3+2x^2 &= 0&& \text{simplify left side} \\[1 em]-3x^3+2x^2+x+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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