Question
$$\frac{5}{x-2}+\frac{4}{x} = \frac{7}{3x}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{5}{x-2}+\frac{4}{x} &= \frac{7}{3x}&& \text{multiply ALL terms by } \color{blue}{ (x-2)x\cdot3 }. \\[1 em](x-2)x\cdot3\cdot\frac{5}{x-2}+(x-2)x\cdot3\cdot\frac{4}{x} &= (x-2)x\cdot3\cdot\frac{7}{3x}&& \text{cancel out the denominators} \\[1 em]15x+12x-24 &= 7x^3-14x^2&& \text{simplify left side} \\[1 em]27x-24 &= 7x^3-14x^2&& \text{move all terms to the left hand side } \\[1 em]27x-24-7x^3+14x^2 &= 0&& \text{simplify left side} \\[1 em]-7x^3+14x^2+27x-24 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver