# How do you find the domain of the function f(x)= x/(x^2+2x-3)?

Apr 10, 2015

Don't take even roots of negative numbers. -- No probhem there are no roots at all.

Don't try9 to divide by $0$. There is a division, so we need to make sure that ${x}^{2} + 2 x - 3$ is not $0$.

OK, so when is it $0$?

Solve ${x}^{2} + 2 x - 3 = 0$

$\left(x + 3\right) \left(x - 1\right) = 0$

$x = - 3 , 1$

These are the numbers we need to throw out of the domain. So tlhe domain is all real numbers except $- 3 , 1.$

(In interval notation: $\left(- \infty , - 3\right) \cup \left(- 3 , 1\right) \cup \left(1 , \infty\right)$)