# How do you find the domain of f(x) = 2 / (1 - x²)?

Mar 12, 2017

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- 1 , 1\right\}$

#### Explanation:

We need

${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

We cannot divide by $0$

The denominator must be different to $0$

$1 - {x}^{2} = \left(1 + x\right) \left(1 - x\right)$

Therefore,

$x \ne - 1$ and $x \ne 1$

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R} - \left\{- 1 , 1\right\}$