Chapter 8: 548 - Review Exercises (page 1026)

Add and Subtract Rational Expressions whose Denominators are Opposites
In the following exercises, add and subtract.
$\frac{a^{2} + 3 a}{a^{2} - 16} - \frac{3 a + 8}{16 - a^{2}} .$

Short Answer

Expert verified

The answer is $\frac{a + 2}{a - 4} .$

Step by step solution

Step 1. Given Information.

Given:

$\frac{a^{2} + 3 a}{a^{2} - 16} - \frac{3 a + 8}{16 - a^{2}}$ having the same denominator just with opposite signs.

Step 2. Creating the denominator exactly same.

Now take a minus sign out of denominator of second term in the above expression we get:

$\frac{a^{2} + 3 a}{a^{2} - 16} + \frac{3 a + 8}{a^{2} - 16}$

Now we can clearly see that the denominators are same.

Step 3. Solving the expression in step 2.

Now as the denominators are same so we can directly subtract the numerators:

$\frac{a^{2} + 3 a}{a^{2} - 16} + \frac{3 a + 8}{a^{2} - 16} = \frac{a^{2} + 3 a + 3 a + 8}{a^{2} - 16} = \frac{a^{2} + 6 a + 8}{a^{2} - 16} = \frac{(a + 2) (a + 4)}{(a - 4) (a + 4)} = \frac{a + 2}{a - 4} .$

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.

Add and Subtract Rational Expressions whose Denominators are Opposites
In the following exercises, add and subtract.
$\frac{a^{2} + 3 a}{a^{2} - 16} - \frac{3 a + 8}{16 - a^{2}} .$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Creating the denominator exactly same.

Step 3. Solving the expression in step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Add and Subtract Rational Expressions whose Denominators are OppositesIn the following exercises, add and subtract.a2+3aa2-16-3a+816-a2.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Creating the denominator exactly same.

Step 3. Solving the expression in step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Add and Subtract Rational Expressions whose Denominators are Opposites
In the following exercises, add and subtract.
$\frac{a^{2} + 3 a}{a^{2} - 16} - \frac{3 a + 8}{16 - a^{2}} .$