Question
$$\frac{x^2-1}{x^3-7x+6} = 0$$
Answer
$$ \begin{matrix}x_1 = 1 & x_2 = -1 \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} \frac{x^2-1}{x^3-7x+6} &= 0&& \text{multiply ALL terms by } \color{blue}{ x^3-7x+6 }. \\[1 em](x^3-7x+6)\frac{x^2-1}{x^3-7x+6} &= (x^3-7x+6)\cdot0&& \text{cancel out the denominators} \\[1 em]x^2-1 &= 0&& \\[1 em] \end{aligned} $$
$ x^{2}-1 = 0 $ is a quadratic equation.
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