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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset Vaia Explanations$ Math

Student Edition · 801 pages

ISBN: 9780078884801

Chapter 11: Q21. (page 728)

Simplify each expression.
$\frac{x + 4}{x^{2} + 12 x + 32}$

Short Answer

Expert verified

The given expression can be simplified to $\frac{1}{x + 8}$ .

Step by step solution

01

Step 1. Simplify rational function.

Let $x, y$ , and $z$ , be polynomials with $x \neq 0$ and $z \neq 0$ .

$\frac{y x}{z x} = \frac{y \cdot x}{z \cdot x} = \frac{y}{z}$

02

Step 2. Factor.

Factor denominator.

$\frac{x + 4}{(x + 4) (x + 8)}$

03

Step 3. Divide.

Divide out common factors.
$\frac{1}{x + 8}$

Therefore, the given expression can be simplified to $\frac{1}{x + 8}$ .

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