$$ \begin{aligned} 2 \cdot \frac{x}{x^3-5x^2}+\frac{2}{x^2+5x} &= 0&& \text{multiply ALL terms by } \color{blue}{ (x^3-5x^2)(x^2+5x) }. \\[1 em](x^3-5x^2)(x^2+5x)\cdot2 \cdot \frac{x}{x^3-5x^2}+(x^3-5x^2)(x^2+5x)\cdot\frac{2}{x^2+5x} &= (x^3-5x^2)(x^2+5x)\cdot0&& \text{cancel out the denominators} \\[1 em]2x^3+10x^2+2x^3-10x^2 &= 0&& \text{simplify left side} \\[1 em]4x^3 &= 0&& \\[1 em] \end{aligned} $$

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