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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. 336 (page 982)

In the following exercises, solve.
$\frac{m}{m + 5} = \frac{50}{m^{2} - 25} + 6$

Short Answer

Expert verified

The solution is $m = - 3, 2 .$

Step by step solution

01

Step 1. Given Information

The given rational equation is $\frac{m}{m + 5} = \frac{50}{m^{2} - 25} + 6$

02

Step 2. Least common Denominator(LCD)

The LCD of the equation is $(m + 5) (m - 5)$

Multiply the equation by LCD,

localid="1647797171568" $(m + 5) (m - 5) \frac{m}{m + 5} = [\frac{50}{m^{2} - 25} + 6] (m + 5) (m - 5) m (m - 5) = 50 + 6 (m + 5) (m - 5) m^{2} - 5 m = 50 + 6 (m^{2} - 25) m^{2} - 5 m = 50 + 6 m^{2} - 25 5 m^{2} + 5 m - 25 = 0 5 (m^{2} + m - 5) = 0$

03

Step 3. Solution of the equation

On simplifying,

$5 (m^{2} + m - 5) = 0 5 (m^{2} + 3 m - 2 m - 5) = 0 5 (m + 3) (m - 2) = 0$

Using the Zero product property,

$m + 3 = 0; m - 2 = 0 m = - 3, m = 2$

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