Chapter 8: Q. 270 (page 966)

In the following exercises, simplify.
$\frac{4 - \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Short Answer

Expert verified

The simplified form of the given expression is $\frac{16 (b - 6)}{(b - 4) (b - 1)}$ .

Step by step solution

Step 1. Given information.

The given expression is:

$\frac{4 - \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B} \div \frac{C}{D} = \frac{A}{B} \cdot \frac{D}{C}$

Step 3. Rewrite the expression.

Simplify the numerator and denominator.

$= \frac{\frac{4 (b - 5) - 4}{b - 5}}{\frac{4 + b (b - 5)}{4 (b - 5)}} = \frac{\frac{4 b - 20 - 4}{b - 5}}{\frac{4 + b^{2} - 5 b}{4 (b - 5)}} = \frac{\frac{4 b - 24}{b - 5}}{\frac{b^{2} - 5 b + 4}{4 (b - 5)}} = \frac{4 b - 24}{b - 5} \div \frac{b^{2} - 5 b + 4}{4 (b - 5)}$

Step 4. Simplify the expression.

Rewrite as the product of first times the reciprocal of the second.

$= \frac{4 b - 24}{b - 5} \cdot \frac{4 (b - 5)}{b^{2} - 5 b + 4} = \frac{4 (b - 6)}{b - 5} \cdot \frac{4 (b - 5)}{b^{2} - 4 b - b + 4} = \frac{4 (b - 6)}{b - 5} \cdot \frac{4 (b - 5)}{b (b - 4) - 1 (b - 4)} = \frac{4 (b - 6)}{b - 5} \cdot \frac{4 (b - 5)}{(b - 4) (b - 1)} = \frac{16 (b - 6)}{(b - 4) (b - 1)}$

Step 5. Conclusion.

The simplified form of the given expression is $\frac{16 (b - 6)}{(b - 4) (b - 1)}$ .

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.

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.

In the following exercises, simplify.
$\frac{4 - \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept.

Step 3. Rewrite the expression.

Step 4. Simplify the expression.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.4-4b-51b-5+b4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept.

Step 3. Rewrite the expression.

Step 4. Simplify the expression.

Step 5. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, simplify.
$\frac{4 - \frac{4}{b - 5}}{\frac{1}{b - 5} + \frac{b}{4}}$