Question
$$\frac{2x^3+7x+33}{x^3}+x^2-11x = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2x^3+7x+33}{x^3}+x^2-11x &= 0&& \text{multiply ALL terms by } \color{blue}{ x^3 }. \\[1 em]x^3\frac{2x^3+7x+33}{x^3}+x^3x^2-x^3\cdot11x &= x^3\cdot0&& \text{cancel out the denominators} \\[1 em]2x^3+7x+33+x^5-11x^4 &= 0&& \text{simplify left side} \\[1 em]x^5-11x^4+2x^3+7x+33 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Equations Solver