Chapter 8: Q. 337 (page 982)

In the following exercises, solve.
$\frac{n}{n + 2} = \frac{8}{n^{2} - 4} + 3$

Short Answer

Expert verified

The solution is $n = 1, - 2$

Step by step solution

Step 1. Given Information

The rational equation is given as:

$\frac{n}{n + 2} = \frac{8}{n^{2} - 4} + 3$

Step 2. Least Common Denominator(LCD)

The LCD of the equation is $(n + 2) (n - 2)$

Multiply the equation by the LCD,

$(n + 2) (n - 2) \frac{n}{n + 2} = [\frac{8}{n^{2} - 4} + 3] (n + 2) (n - 2) n (n - 2) = 8 + 3 (n + 2) (n - 2) n^{2} - 2 n = 8 + 3 (n^{2} - 4) n^{2} - 2 n = 8 + 3 n^{2} - 12 2 n^{2} + 2 n - 4 = 0 2 (n^{2} + n - 2) = 0$

Step 3. Solution of the equation

The equation can be factored as,

$2 (n^{2} + n - 2) = 0 2 (n^{2} + 2 n - n - 2) = 0 2 (n + 2) (n - 1) = 0$

Using the Zero product property,

$n + 2 = 0, n - 1 = 0 n = - 2, n = 1 .$

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In the following exercises, solve.
$\frac{n}{n + 2} = \frac{8}{n^{2} - 4} + 3$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator(LCD)

Step 3. Solution of the equation

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In the following exercises, solve.nn+2=8n2-4+3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Least Common Denominator(LCD)

Step 3. Solution of the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Theoretical and Mathematical Physics

Probability and Statistics

Geometry

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve.
$\frac{n}{n + 2} = \frac{8}{n^{2} - 4} + 3$