# How do you find the domain for H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2)?

Jul 6, 2018

$\left(- \infty , 0\right) \cup \left(0 , 4\right) \cup \left(4 , \infty\right)$

#### Explanation:

The denominator of h(x) cannot be zero as this would make h(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.

$\text{solve } x {\left(x - 4\right)}^{2} = 0$

$\Rightarrow x = 0 \text{ and "x=4larrcolor(red)"excluded values}$

$\text{domain } x \in \left(- \infty , 0\right) \cup \left(0 , 4\right) \cup \left(4 , \infty\right)$
graph{((x-1)(x+2)(x-3))/(x(x-4)^2) [-10, 10, -5, 5]}