Q20. Find the quotient.x2+7x+12x2鈭�2... [FREE SOLUTION]

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q20. (page 699)

Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25} 梅 \frac{x^{2} 鈭� 9}{2 x + 10}$

Short Answer

Expert verified

The final answer is $\frac{2 (x + 4)}{(x 鈭� 5) (x 鈭� 3)}$ .

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q 鈮� 0$ .

Step 2. Define the quotient of two expressions ab and cd.

The quotient of two expressions $\frac{a}{b}$ and $\frac{c}{d}$ , where $b 鈮� 0$ and $d 鈮� 0$ , is given below.

$\frac{a}{b} 梅 \frac{c}{d} = \frac{a}{b} 脳 \frac{d}{c} = \frac{a c}{b d} 鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌夆赌� ........... (1)$

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

Use $(1)$ to find the quotient $\frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25} 梅 \frac{x^{2} 鈭� 9}{2 x + 10}$ .

role="math" localid="1648030191290" $\begin{array}{r} \frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25} 梅 \frac{x^{2} 鈭� 9}{2 x + 10} = (\frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25}) 脳 (\frac{2 x + 10}{x^{2} 鈭� 9}) \\ = \frac{(x^{2} + 7 x + 12) (2 x + 10)}{(x^{2} 鈭� 25) (x^{2} 鈭� 9)} \\ = \frac{(x^{2} + 4 x + 3 x + 12) [2 (x + 5)]}{(x^{2} 鈭� 5^{2}) (x^{2} 鈭� 9)} \\ = \frac{[x (x + 4) + 3 (x + 4)] [2 (x + 5)]}{(x + 5) (x 鈭� 5) (x + 3) (x 鈭� 3)} \\ = \frac{(x + 4) (x + 3) (2) (x + 5)}{(x + 5) (x 鈭� 5) (x + 3) (x 鈭� 3)} \\ = \frac{2 (x + 4)}{(x 鈭� 5) (x 鈭� 3)} \end{array}$

Therefore, the final answer is $\frac{2 (x + 4)}{(x 鈭� 5) (x 鈭� 3)}$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

$x$	1	4	8	12
$y$	2	8	16	24

91影视

Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25} 梅 \frac{x^{2} 鈭� 9}{2 x + 10}$

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the quotient of two expressions ab and cd.

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

91影视

Find the quotient.x2+7x+12x2鈭�25梅x2鈭�92x+10

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the quotient of two expressions ab and cd.

Step 3. Calculate the quotient x2+7x+12x2−25÷x2−92x+10.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the quotient.
$\frac{x^{2} + 7 x + 12}{x^{2} 鈭� 25} 梅 \frac{x^{2} 鈭� 9}{2 x + 10}$