$$5 \cdot \frac{r+2}{r^2}+11r+18 = 0$$
Answer
$$ \begin{matrix}r_1 = -1.68647 & r_2 = 0.02505+0.73377i & r_3 = 0.02505-0.73377i \end{matrix} $$
Explanation
$$ \begin{aligned} 5 \cdot \frac{r+2}{r^2}+11r+18 &= 0&& \text{multiply ALL terms by } \color{blue}{ r^2 }. \\[1 em]r^2\cdot5 \cdot \frac{r+2}{r^2}+r^2\cdot11r+r^2\cdot18 &= r^2\cdot0&& \text{cancel out the denominators} \\[1 em]5r+10+11r^3+18r^2 &= 0&& \text{simplify left side} \\[1 em]11r^3+18r^2+5r+10 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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