Chapter 11: Q4. (page 731)

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

Short Answer

Expert verified

$\frac{1}{y (x - 3)}$

Step by step solution

Step 1. Dividing rational expression.

Let $x, y, z$ and $w$ be polynomials with $y, z, w \neq 0$ , then, $\frac{x}{y} \div \frac{z}{w} = \frac{x}{y} \cdot \frac{w}{z} = \frac{x w}{y z}$ .

Step 2. Divide.

Divide by the common factors.

$\frac{(x + 3)}{y^{2}} \div \frac{x^{2} - 9}{y} = \frac{(x + 3)}{y^{2}} \cdot \frac{y}{x^{2} - 9}$

Step 3. Simplify.

Simplify the above obtained expression.

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

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Step 1. Dividing rational expression.

Step 2. Divide.

Step 3. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

Find each product or quotient.x+3y2÷x2−9y

Short Answer

Step by step solution

Step 1. Dividing rational expression.

Step 2. Divide.

Step 3. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Discrete Mathematics

Applied Mathematics

Statistics

Calculus

Study anywhere. Anytime. Across all devices.

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