Question
$$\frac{x^4+1}{x^3+x} = \frac{7}{2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{x^4+1}{x^3+x} &= \frac{7}{2}&& \text{multiply ALL terms by } \color{blue}{ (x^3+x)\cdot2 }. \\[1 em](x^3+x)\cdot2 \cdot \frac{x^4+1}{x^3+x} &= (x^3+x)\cdot2\cdot\frac{7}{2}&& \text{cancel out the denominators} \\[1 em]2x^4+2 &= 7x^3+7x&& \text{move all terms to the left hand side } \\[1 em]2x^4+2-7x^3-7x &= 0&& \text{simplify left side} \\[1 em]2x^4-7x^3-7x+2 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Equations Solver