Question
$$x^3-\frac{1}{x+2} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^3-\frac{1}{x+2} &= 0&& \text{multiply ALL terms by } \color{blue}{ x+2 }. \\[1 em](x+2)x^3-(x+2)\cdot\frac{1}{x+2} &= (x+2)\cdot0&& \text{cancel out the denominators} \\[1 em]x^4+2x^3-1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver