Question
$$2 \cdot \frac{x}{x^2}-9 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 2 \cdot \frac{x}{x^2}-9 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^2 }. \\[1 em]x^2\cdot2 \cdot \frac{x}{x^2}-x^2\cdot9 &= x^2\cdot0&& \text{cancel out the denominators} \\[1 em]\frac{2}{x^1}-9x^2 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot\frac{2}{x^1}-x^1\cdot9x^2 &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]2-9x^3 &= 0&& \text{simplify left side} \\[1 em]-9x^3+2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver