$$\frac{2x}{5x+1}+\frac{x}{x-6} = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 11 }{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{2x}{5x+1}+\frac{x}{x-6} &= 0&& \text{multiply ALL terms by } \color{blue}{ (5x+1)(x-6) }. \\[1 em](5x+1)(x-6)\frac{2x}{5x+1}+(5x+1)(x-6)\frac{x}{x-6} &= (5x+1)(x-6)\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-12x+5x^2+x &= 0&& \text{simplify left side} \\[1 em]7x^2-11x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 7x^{2}-11x = 0 } $, first we need to factor our $ x $.
$$ 7x^{2}-11x = x \left( 7x-11 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ 7x-11 = 0$.
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