what's the truth value of this statement

Question

$$\forall x\in\mathbb R\quad \frac{x^2+2}{x^2-1}\in\mathbb R$$ I thought of making the equation equal to zero then solve it, but I don't think this would be right. I am having a difficulty finding the truth value of this statement, any help?

Answer 1

$\forall x\in\mathbb{R}(\frac{x^2+2}{x^2-1}\in\mathbb{R})$

$\implies\frac{1^2+2}{1^2-1}\in\mathbb{R}$

$\iff\frac{1+2}{1-1}\in\mathbb{R}$

$\iff\frac{3}{0}\in\mathbb{R}$

$\iff$ false