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