I am having trouble finding the domain of
x^3 + 5x
------------
x^2 - 6x + 8
Thanks for your Help
Limitations on the domain of a function take the form of zeros in the denominator, negative numbers under a square root sign, and the like. Here we have a fraction so we want to look at where the denominator goes to zero.
$\displaystyle x^2 - 6x + 8 = (x - 4)(x - 2) = 0$
So the denominator is zero at x = 2 and x = 4. Thus these values for x cannot be in the domain. This is our only restriction, so the domain will be:
$\displaystyle ( -\infty, 2) \cup (2, 4) \cup (4, \infty)$
or, more simply, "all real x except 2 and 4."
-Dan