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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 8: Q. 566 (page 1027)

In the following exercises, subtract and add.
$\frac{n}{n + 3} + \frac{2}{n - 3} - \frac{n - 9}{n^{2} - 9}$

Short Answer

Expert verified

On simplifying the given expression, we get,

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

Step by step solution

01

Step 1. Given information.

Consider the given question,

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

02

Step 2. Find the LCD of the denominators.

Rewrite the given expression,

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

Rewrite the rational expression as an equivalent rational expression with the LCD,

$= \frac{n (n - 3)}{(n - 3) (n + 3)} + \frac{2 (n + 3)}{(n - 3) (n + 3)} - \frac{n - 9}{(n - 3) (n + 3)} = \frac{n^{2} - 3 n}{(n - 3) (n + 3)} + \frac{2 n + 6}{(n - 3) (n + 3)} - \frac{n - 9}{(n - 3) (n + 3)} = \frac{n^{2} - 3 n + 2 n + 6 - n + 9}{(n - 3) (n + 3)} = \frac{n^{2} - 2 n + 15}{(n - 3) (n + 3)} = \frac{n^{2} - 2 n + 15}{(n - 3) (n + 3)}$

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