# How do you find the limit of R(x) = (x - 1)/(x² - 1) as x approaches -1?

Nov 2, 2016

You need to manipulate the denominator and simplify before evaluating the limit

#### Explanation:

Using that ${x}^{2} - 1 = \left(x + 1\right) \left(x - 1\right)$, we can write:

$R \left(x\right) = \frac{x - 1}{\left(x + 1\right) \left(x - 1\right)}$ we can then simplify and we have:

$R \left(x\right) = \frac{1}{x + 1}$, so we have:

${\lim}_{x \rightarrow - 1} R \left(x\right) = {\lim}_{x \rightarrow - 1} \frac{1}{x + 1} = \infty$