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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. 554 (page 1026)

In the following exercises, rewrite as equivalent rational expressions with the given denominator.
$(m + 2) (m 鈭� 5) (m + 4)$
$\frac{4}{m^{2} - 3 m - 10}, \frac{2 m}{m^{2} - m - 20}$

Short Answer

Expert verified

$\frac{4}{(m - 5) (m + 2)}, \frac{2 m}{(m - 5) (m + 4)}$

Step by step solution

01

Step 1. Given Information.

The given expression is:

$\frac{4}{m^{2} - 3 m - 10}, \frac{2 m}{m^{2} - m - 20}$

02

Step 2. Factorization.

$c o n s i d e r, m^{2} - 3 m - 10 m^{2} - 5 m + 2 m - 10 m (m - 5) + 2 (m - 5) (m + 2) (m - 5) N o w, c o n s i d e r m^{2} - m - 20 m^{2} - 5 m + 4 m - 20 m (m - 5) + 4 (m - 5) (m + 4) (m - 5)$

03

Step 3. Final Expression.

The given rational expression can be written as:

$\frac{4}{m^{2} - 3 m - 10}, \frac{2 m}{m^{2} - m - 20} \frac{4}{(m - 5) (m + 2)}, \frac{2 m}{(m - 5) (m + 4)}$

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