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.

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

Now on simplifying the numerator we get

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

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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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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

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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.