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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. 564 (page 1026)

In the following exercises, subtract and add.
$\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}$

Short Answer

Expert verified

On simplifying the given expression, we get,

$\frac{1 - w}{4 - w}$

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\frac{- 3 w - 15}{w^{2} + w - 20} - \frac{w + 2}{4 - w}$

02

Step 2. Find the LCD of the denominators.

Rewrite the given expression,

$= \frac{- 3 (w + 5)}{(w - 4) (w + 5)} - \frac{w + 2}{4 - w} = \frac{3 (w + 5)}{(4 - w) (w + 5)} - \frac{w + 2}{4 - w}$

Take out the common term,

$= \frac{3}{4 - w} - \frac{w + 2}{4 - w}$

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

$= \frac{1 - w}{4 - w}$

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