Q. 254 Simplify the expression 4n2+6n+9... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 254 (page 955)

Simplify the expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ and explain all your steps.

Short Answer

Expert verified

The expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ is simplified as $\frac{3 n - 15}{(n + 3) (n + 3) (n - 3)}$ .

Step by step solution

Step 1. Given Information

We are given an expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ .

We need to simplify the expression.

Step 2. Find the LCD

In the expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ , the denominators can be factored as

role="math" localid="1653585283061" $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9} = \frac{4}{(n + 3) (n + 3)} - \frac{1}{(n + 3) (n - 3)}$

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

Step 3. Subtract the fractions

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

$\frac{4}{(n + 3) (n + 3)} - \frac{1}{(n + 3) (n - 3)} = \frac{4 路 (n - 3)}{(n + 3) (n + 3) (n - 3)} - \frac{1 路 (n + 3)}{(n + 3) (n - 3) (n + 3)}$

Now on simplifying the numerator we get

$\begin{array}{rcl} \frac{4 路 (n - 3)}{(n + 3) (n + 3) (n - 3)} - \frac{1 路 (n + 3)}{(n + 3) (n - 3) (n + 3)} & = & \frac{4 n - 12 - (n + 3)}{(n + 3) (n + 3) (n - 3)} \\ = & \frac{4 n - 12 - n - 3}{(n + 3) (n + 3) (n - 3)} \\ = & \frac{3 n - 15}{(n + 3) (n + 3) (n - 3)} \end{array}$

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91影视

Simplify the expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ and explain all your steps.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the LCD

Step 3. Subtract the fractions

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91影视

Simplify the expression 4n2+6n+9-1n2-9and explain all your steps.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find the LCD

Step 3. Subtract the fractions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Simplify the expression $\frac{4}{n^{2} + 6 n + 9} - \frac{1}{n^{2} - 9}$ and explain all your steps.