Chapter 8: Q 122. (page 931)

Divide Rational Expressions: $\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$

Short Answer

Expert verified

The required answer is $\frac{(n + 8) (n - 1)}{3 (n - 5) (9 n - 2)}$ .

Step by step solution

Step 1. Given information.

The given expression is $\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$ .

Step 2. Simplify the expression.

$\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$

Apply the fraction rule.

$\frac{\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} (n + 6)}{108 n^{2} - 24 n} = \frac{\frac{(4 n^{2} + 32 n) (3 n + 2) (n - 1) (n + 6)}{(3 n + 2) (n^{2} + n - 30)}}{108 n^{2} - 24 n} = \frac{\frac{(4 n^{2} + 32 n) (3 n + 2) (n - 1) (n + 6)}{(3 n + 2) (n - 5) (n + 6)}}{108 n^{2} - 24 n} = \frac{(4 n^{2} + 32 n) (n - 1)}{(n - 5) (108 n^{2} - 24 n)}$

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

$\frac{(4 n^{2} + 32 n) (n - 1)}{(n - 5) (108 n^{2} - 24 n)} = \frac{4 n (n + 8) (n - 1)}{(n - 5) \cdot 12 n (9 n - 2)} = \frac{4 (n + 8) (n - 1)}{(n - 5) \cdot 4 \cdot 3 (9 n - 2)} = \frac{(n + 8) (n - 1)}{3 (n - 5) (9 n - 2)}$

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.

Divide Rational Expressions: $\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$

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

Probability and Statistics

Mechanics Maths

Decision Maths

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Company

Product

Help

Divide Rational Expressions: 4n2 + 32n3n + 2×3n2 − n − 2n2 + n − 30 ÷108n2 − 24nn + 6

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

Probability and Statistics

Mechanics Maths

Decision Maths

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Divide Rational Expressions: $\frac{4 n^{2} + 32 n}{3 n + 2} \times \frac{3 n^{2} - n - 2}{n^{2} + n - 30} \div \frac{108 n^{2} - 24 n}{n + 6}$