Q 123. Divide Rational Expressions:聽12... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q 123. (page 931)

Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

Short Answer

Expert verified

The required answer is $\frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

Step 2. Simplify the expression.

$\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

Apply the fraction rule.

$\frac{\frac{12 p^{2} + 3 p}{p + 3}}{\frac{p^{2} + 2 p - 63}{p^{2} - p - 12}} 脳 \frac{p - 7}{9 p^{3} - 9 p^{2}} = \frac{(12 p^{2} + 3 p) (p^{2} - p - 12) (p - 7)}{(p + 3) (p^{2} + 2 p - 63) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4) (p + 3) (p - 7)}{(p + 3) (p^{2} + 2 p - 63) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p^{2} + 2 p - 63) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4) (p - 7)}{(p - 7) (p + 9) (9 p^{3} - 9 p^{2})} = \frac{(12 p^{2} + 3 p) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})}$

Step 3. Factor the numerators and denominators and then multiply.

$= \frac{3 p (4 p + 1) (p - 4)}{(p + 9) (9 p^{3} - 9 p^{2})} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 9 p^{2} (p - 1)} = \frac{3 p (4 p + 1) (p - 4)}{(p + 9) 脳鈥� 3 脳鈥� 3 p^{2} (p - 1)} = \frac{(4 p + 1) (p - 4)}{(p + 9) 脳鈥� 3 p (p - 1)} = \frac{(4 p + 1) (p - 4)}{3 p (p + 9) (p - 1)}$

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.

91影视

Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

91影视

Divide Rational Expressions:12p2鈥�+鈥�3pp鈥�+鈥�3梅p2+鈥�2p鈥�鈭�鈥�63p2鈥�鈭�鈥�p鈥�鈭�鈥�12鈥�鈥�脳p鈥�鈭�鈥�79p3鈥�鈭�鈥�9p2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the expression.

Step 3. Factor the numerators and denominators and then multiply.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\{\frac{12 p^{2} 鈥� + 鈥� 3 p}{p 鈥� + 鈥� 3} 梅 \frac{p^{2} + 鈥� 2 p 鈥� 鈭� 鈥� 63}{p^{2} 鈥� 鈭� 鈥� p 鈥� 鈭� 鈥� 12}\} 鈥� 鈥� 脳 \frac{p 鈥� 鈭� 鈥� 7}{9 p^{3} 鈥� 鈭� 鈥� 9 p^{2}}$