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Q. 15

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Found in: Page 225

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Find the domain of the rational function. $\frac{-4{x}^{2}}{\left(x-2\right)\left(x+4\right)}$

The domain of the given function is $\left(-\infty , -4\right)\cup \left(-4, 2\right)\cup \left(2, \infty \right)$

See the step by step solution

## Step 1. Given information

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

## Step 2. Find the domain

For the domain, the denominator should not be equal to zero.

So,

$\left(x-2\right)\left(x+4\right)\ne 0\phantom{\rule{0ex}{0ex}}x-2\ne 0\phantom{\rule{0ex}{0ex}}x\ne 2\phantom{\rule{0ex}{0ex}}or\phantom{\rule{0ex}{0ex}}x+4\ne 0\phantom{\rule{0ex}{0ex}}x\ne -4$

Thus, the domain of the given function is all real numbers except $2$ and $-4$

Therefore, the domain is localid="1646074172973" $\left(-\infty , -4\right)\cup \left(-4, 2\right)\cup \left(2, \infty \right)$