Question
$$\frac{2}{3x-1}+\frac{3}{3x+1} = \frac{5}{3}x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2}{3x-1}+\frac{3}{3x+1} &= \frac{5}{3}x&& \text{multiply ALL terms by } \color{blue}{ (3x-1)(3x+1)\cdot3 }. \\[1 em](3x-1)(3x+1)\cdot3\cdot\frac{2}{3x-1}+(3x-1)(3x+1)\cdot3\cdot\frac{3}{3x+1} &= (3x-1)(3x+1)\cdot3 \cdot \frac{5}{3}x&& \text{cancel out the denominators} \\[1 em]18x+6+27x-9 &= 45x^3-5x&& \text{simplify left side} \\[1 em]45x-3 &= 45x^3-5x&& \text{move all terms to the left hand side } \\[1 em]45x-3-45x^3+5x &= 0&& \text{simplify left side} \\[1 em]-45x^3+50x-3 &= 0&& \\[1 em] \end{aligned} $$
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