$$\frac{x}{2x-3} = 3 \cdot \frac{x}{x+11}$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 4 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x}{2x-3} &= 3 \cdot \frac{x}{x+11}&& \text{multiply ALL terms by } \color{blue}{ (2x-3)(x+11) }. \\[1 em](2x-3)(x+11)\frac{x}{2x-3} &= (2x-3)(x+11)\cdot3 \cdot \frac{x}{x+11}&& \text{cancel out the denominators} \\[1 em]x^2+11x &= 6x^2-9x&& \text{move all terms to the left hand side } \\[1 em]x^2+11x-6x^2+9x &= 0&& \text{simplify left side} \\[1 em]-5x^2+20x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -5x^{2}+20x = 0 } $, first we need to factor our $ x $.
$$ -5x^{2}+20x = x \left( -5x+20 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ -5x+20 = 0$.
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