Chapter 7: Q. 420 (page 736)

In the following exercises, perform the indicated operations
$\frac{n}{n + 3} + \frac{2}{n - 3} - \frac{n - 9}{n^{2} - 9}$

Short Answer

Expert verified

The simplified expression is $\frac{n - 5}{n - 3}$

Step by step solution

Step 1. Given information

Expression:

$\frac{n}{n + 3} + \frac{2}{n - 3} - \frac{n - 9}{n^{2} - 9}$

Step 2. Find LCD

Denominator of the first fraction is $n + 3$

Denominator of the second fraction is $n - 3$

Denominator of the third fraction is $n^{2} - 9$

It can be factorize as

$n^{2} - 9 = n^{2} - 3^{2} = (n - 3) (n + 3)$

So LCD is $(n - 3) (n + 3)$

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

$\frac{n (n - 3)}{(n + 3) (n - 3)} + \frac{2 (n + 3)}{(n - 3) (n + 3)} - \frac{n - 9}{(n - 3) (n + 3)}$

Step 4.Simplify the numerators and perform operations

$\frac{(n^{2} - 3 n)}{(n + 3) (n - 3)} + \frac{(2 n + 6)}{(n + 3) (n - 3)} - \frac{(n - 9)}{(n + 3) (n - 3)} = \frac{(n^{2} - 3 n) + (2 n + 6) - (n - 9)}{(n + 3) (n - 3)} = \frac{n^{2} - 3 n + 2 n + 6 - n + 9}{(n + 3) (n - 3)}$

Step 5. Simplify numerators

$\frac{n^{2} - 2 n + 15}{(n + 3) (n - 3)}$

Step 6. factorize numerator

$\frac{n^{2} - 5 n + 3 n + 15}{(n + 3) (n - 3)} = \frac{n (n - 5) + 3 (n - 5)}{(n + 3) (n - 3)} = \frac{(n - 5) (n + 3)}{(n + 3) (n - 3)}$

Step 7. Cancel common factors

$\frac{n - 5}{n - 3}$

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 the indicated operations
$\frac{n}{n + 3} + \frac{2}{n - 3} - \frac{n - 9}{n^{2} - 9}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators and perform operations

Step 5. Simplify numerators

Step 6. factorize numerator

Step 7. Cancel common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations nn+3+2n-3-n-9n2-9

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find LCD

Step 3. Rewrite each rational expression as an equivalent rational expression with the LCD

Step 4.Simplify the numerators and perform operations

Step 5. Simplify numerators

Step 6. factorize numerator

Step 7. Cancel common factors

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In the following exercises, perform the indicated operations
$\frac{n}{n + 3} + \frac{2}{n - 3} - \frac{n - 9}{n^{2} - 9}$