# What is the domain and range of  y = x^2 / (x^2 - 1)?

May 10, 2018

Below

#### Explanation:

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

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

$y = 1 + \frac{1}{{x}^{2} - 1}$

$y = 1 + \frac{1}{\left(x - 1\right) \left(x + 1\right)}$

Domain: all reals except when $x = 1$ and $x = - 1$
Range: all reals except when $y = 1$

You can verify by looking at the graph.

graph{x^2/(x^2-1) [-10, 10, -5, 5]}