Question
$$\frac{1}{x}+\frac{5}{x(x-5)} = 0$$
Answer
$$ \begin{matrix}x_1 = 5 & x_2 = \dfrac{ 24 }{ 5 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{1}{x}+\frac{5}{x(x-5)} &= 0&& \text{multiply ALL terms by } \color{blue}{ x(x-5) }. \\[1 em]x(x-5)\cdot\frac{1}{x}+x(x-5)\cdot\frac{5}{x(x-5)} &= x(x-5)\cdot0&& \text{cancel out the denominators} \\[1 em]x-5+5x^2-50x+125 &= 0&& \text{simplify left side} \\[1 em]5x^2-49x+120 &= 0&& \\[1 em] \end{aligned} $$
$ 5x^{2}-49x+120 = 0 $ is a quadratic equation.
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