Question
$$\frac{3}{2}x+\frac{4}{x}+1+\frac{4}{x^2}+x = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{3}{2}x+\frac{4}{x}+1+\frac{4}{x^2}+x &= 0&& \text{multiply ALL terms by } \color{blue}{ 2xx^2 }. \\[1 em]2xx^2\frac{3}{2}x+2xx^2\cdot\frac{4}{x}+2xx^2\cdot1+2xx^2\cdot\frac{4}{x^2}+2xx^2x &= 2xx^2\cdot0&& \text{cancel out the denominators} \\[1 em]3+8+2x^3+\frac{8}{x^1}+2x^4 &= 0&& \text{multiply ALL terms by } \color{blue}{ x^1 }. \\[1 em]x^1\cdot3+x^1\cdot8+x^1\cdot2x^3+x^1\cdot\frac{8}{x^1}+x^1\cdot2x^4 &= x^1\cdot0&& \text{cancel out the denominators} \\[1 em]3x+8x+2x^4+8+2x^5 &= 0&& \text{simplify left side} \\[1 em]2x^5+2x^4+11x+8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Equations Solver