Question
$$\frac{x^{10}+x^5+1}{x-1} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x^{10}+x^5+1}{x-1} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-1 }. \\[1 em](x-1)\frac{x^{10}+x^5+1}{x-1} &= (x-1)\cdot0&& \text{cancel out the denominators} \\[1 em]x^{10}+x^5+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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