Chapter 4.4, Problem 17AYU

In Problems 15-26, find the domain of each rational function

$H\left(x\right)\text{ = }\frac{-4x^2}{\left(x-\text{ 2}\right)\left(x\text{ + 4}\right)}$

To determine

To find: The domain of the rational function.

Answer to Problem 17AYU

Domain is $\left\{x|x\ne -4,x\ne 2\right\}$.

Explanation of Solution

Given:

$H\left(x\right)=\frac{-4x^2}{\left(x-2\right)\left(x+4\right)}$

The domain $H\left(x\right)=\frac{-4x^2}{\left(x-2\right)\left(x+4\right)}$ is the set of all real numbers $x$ except $-4$ and 2; that is, the domain is $\left\{x|x\ne -4,x\ne 2\right\}$.