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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q4. (page 731)

Find each product or quotient.
$\frac{(x + 3)}{y^{2}} 梅 \frac{x^{2} 鈭� 9}{y}$

Short Answer

Expert verified

$\frac{1}{y (x 鈭� 3)}$

Step by step solution

01

Step 1. Dividing rational expression.

Let $x, y, z$ and $w$ be polynomials with $y, z, w 鈮� 0$ , then, $\frac{x}{y} 梅 \frac{z}{w} = \frac{x}{y} 鈰� \frac{w}{z} = \frac{x w}{y z}$ .

02

Step 2. Divide.

Divide by the common factors.

$\frac{(x + 3)}{y^{2}} 梅 \frac{x^{2} 鈭� 9}{y} = \frac{(x + 3)}{y^{2}} 鈰� \frac{y}{x^{2} 鈭� 9}$

03

Step 3. Simplify.

Simplify the above obtained expression.

$\begin{matrix} \frac{(x + 3) y}{y^{2} (x^{2} 鈭� 9)} = \frac{(x + 3)}{y (x + 3) (x 鈭� 3)} \\ = \frac{1}{y (x 鈭� 3)} \end{matrix}$

The product of given expression is $\frac{1}{y (x 鈭� 3)}$ .

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Most popular questions from this chapter

AREA The area of a rectangle is $x^{2} + 5 x + 6$ . What binomial expressions represent the side lengths of the rectangle?

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$\frac{t 鈭� 5}{t 鈭� 6} + \frac{t + 8}{t 鈭� 6}$

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