Question
$$\frac{x^3+x}{x-2} = 12$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x^3+x}{x-2} &= 12&& \text{multiply ALL terms by } \color{blue}{ x-2 }. \\[1 em](x-2)\frac{x^3+x}{x-2} &= (x-2)\cdot12&& \text{cancel out the denominators} \\[1 em]x^3+x &= 12x-24&& \text{move all terms to the left hand side } \\[1 em]x^3+x-12x+24 &= 0&& \text{simplify left side} \\[1 em]x^3-11x+24 &= 0&& \\[1 em] \end{aligned} $$
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