Chapter 7: Q. 115 (page 668)

In the following exercises, perform indicated operations.
$\frac{5 b}{a^{2} b - 2 a^{2}} + \frac{2 b}{b^{2} - 4}$

Short Answer

Expert verified

The resultant expression is $\frac{b (5 b + 10 + 2 a^{2})}{a^{2} (b - 2) (b + 2)}$ .

Step by step solution

Step 1. Given Information

The given expression is $\frac{5 b}{a^{2} b - 2 a^{2}} + \frac{2 b}{b^{2} - 4}$ .

Step 2. Express with common denominator

Factor the denominators of the given expression.

$\frac{5 b}{a^{2} (b - 2)} + \frac{2 b}{(b + 2) (b - 2)}$

The LCD of the terms of obtained expression is $a^{2} (b + 2) (b - 2)$ .
Multiply the numerator and denominator of first term by $(b + 2)$ and second term by $a^{2}$ .

role="math" localid="1645428256449" $\frac{5 b (b + 2)}{a^{2} (b - 2) (b + 2)} + \frac{2 b (a^{2})}{(b + 2) (b - 2) (a^{2})} = \frac{5 b^{2} + 10 b}{a^{2} (b - 2) (b + 2)} + \frac{2 a^{2} b}{a^{2} (b + 2) (b - 2)}$

Step 3. Simplify

As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\frac{5 b^{2} + 10 b + 2 a^{2} b}{a^{2} (b - 2) (b + 2)} = \frac{b (5 b + 10 + 2 a^{2})}{a^{2} (b - 2) (b + 2)}$

So, the resultant expression is $\frac{b (5 b + 10 + 2 a^{2})}{a^{2} (b - 2) (b + 2)}$ .

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.

In the following exercises, perform indicated operations.
$\frac{5 b}{a^{2} b - 2 a^{2}} + \frac{2 b}{b^{2} - 4}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Probability and Statistics

Calculus

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations. 5ba2b-2a2+2bb2-4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Express with common denominator

Step 3. Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Probability and Statistics

Calculus

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, perform indicated operations.
$\frac{5 b}{a^{2} b - 2 a^{2}} + \frac{2 b}{b^{2} - 4}$