Question
$$x \cdot \frac{x-8}{x-8} = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 8 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x \cdot \frac{x-8}{x-8} &= 0&& \text{multiply ALL terms by } \color{blue}{ x-8 }. \\[1 em](x-8)x \cdot \frac{x-8}{x-8} &= (x-8)\cdot0&& \text{cancel out the denominators} \\[1 em]x^2-8x &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ x^{2}-8x = 0 } $, first we need to factor our $ x $.
$$ x^{2}-8x = x \left( x-8 \right) $$$ x = 0 $ is a root of multiplicity $ 1 $.
The second root can be found by solving equation $ x-8 = 0$.
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