$$\frac{1}{x}+\frac{2}{x^2} = \frac{x+9}{2x^2}$$
Answer
$$ \begin{matrix}x_1 = 0.75118 & x_2 = -0.58066 & x_3 = -9.17053 \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{2}{x^2} &= \frac{x+9}{2x^2}&& \text{multiply ALL terms by } \color{blue}{ xx^2\cdot2 }. \\[1 em]xx^2\cdot2\cdot\frac{1}{x}+xx^2\cdot2\cdot\frac{2}{x^2} &= xx^2\cdot2 \cdot \frac{x+9}{2x^2}&& \text{cancel out the denominators} \\[1 em]2+\frac{4}{x^1} &= x^2+9x&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot2+x^1\cdot\frac{4}{x^1} &= x^1\cdot1x^2+x^1\cdot9x&& \text{cancel out the denominators} \\[1 em]2x+4 &= x^3+9x^2&& \text{move all terms to the left hand side } \\[1 em]2x+4-x^3-9x^2 &= 0&& \text{simplify left side} \\[1 em]-x^3-9x^2+2x+4 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Equations Solver