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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. 289 (page 967)

In the following exercises, simplify.
$\frac{\frac{m}{m + 5}}{4 + \frac{1}{m - 5}}$

Short Answer

Expert verified

The simplified expression is $\frac{m (m - 5)}{4 m^{2} + m - 95}$ $\frac{m (m - 5)}{4 m^{2} + m - 95}$

Step by step solution

01

Step 1. Given expression

The given expression is

$\frac{\frac{m}{m + 5}}{4 + \frac{1}{m - 5}}$

02

Step 2. Simplify the expression

$\frac{\frac{m}{m + 5}}{4 + \frac{1}{m - 5}} = \frac{(m + 5) (m - 5) (\frac{m}{(m + 5)})}{(m + 5) (m - 5) (4 + \frac{1}{m - 5})} = \frac{m (m - 5)}{4 (m + 5) (m - 5) + m + 5} = \frac{m (m - 5)}{4 m^{2} + m - 95}$

The simplified expression is $\frac{m (m - 5)}{4 m^{2} + m - 95}$

03

Step 3. The solution

The simplified expression is $\frac{m (m - 5)}{4 m^{2} + m - 95}$

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